완화자 (Korean Wikipedia)

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See (Friedrichs 1944, 136–139쪽). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See the commentary of Peter Lax to the paper (Friedrichs 1944) in (Friedrichs 1986, volume 1, p. 117). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced. Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S., 편집., 《Selecta》, Contemporary Mathematicians, Boston-Basel-Stuttgart: Birkhäuser Verlag, 427 (Vol. 1); pp. 608 (Vol. 2)쪽, ISBN 0-8176-3270-0, Zbl 0613.01020 . A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgag Wasow, Harold Weitzner.
See (Giusti 1984, 11쪽). Giusti, Enrico (1984), 《Minimal surfaces and functions of bounded variations》, Monographs in Mathematics 80, Basel-Boston-Stuttgart: Birkhäuser Verlag, xii+240쪽, ISBN 0-8176-3153-4, MR 0775682, Zbl 0545.49018 .
As when the paper (Friedrichs 1944) was published, few years before Laurent Schwartz widespread his work. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Friedrichs 1944, 136–138쪽), properties PI, PII, PIII and their consequence PIII₀. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
Also, in this respect, Friedrichs (1944, 132쪽) says:-"The main tool for the proof is a certain class of smoothing operators approximating unity, the "mollifiers". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Friedrichs 1944, 137쪽), paragraph 2, "Integral operators". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Hörmander 1990, 14쪽), lemma 1.2.3.: the example is stated in implicit form by first defining $f (t) = exp(-1/ t)$ for $t$ ∈ ℝ⁺, and then considering $f (x) = f (1-| x | 2) = exp(-1/(1-| x | 2))$ for $x$ ∈ ℝⁿ. Hörmander, Lars (1990), 《The analysis of linear partial differential operators I》, Grundlehren der Mathematischen Wissenschaft 256 2판, Berlin-Heidelberg-New York: Springer-Verlag, ISBN 0-387-52343-X, MR 1065136, Zbl 0712.35001 .
See for example (Hörmander 1990). Hörmander, Lars (1990), 《The analysis of linear partial differential operators I》, Grundlehren der Mathematischen Wissenschaft 256 2판, Berlin-Heidelberg-New York: Springer-Verlag, ISBN 0-387-52343-X, MR 1065136, Zbl 0712.35001 .
A proof of this fact can be found in (Hörmander 1990, 25쪽), Theorem 1.4.1. Hörmander, Lars (1990), 《The analysis of linear partial differential operators I》, Grundlehren der Mathematischen Wissenschaft 256 2판, Berlin-Heidelberg-New York: Springer-Verlag, ISBN 0-387-52343-X, MR 1065136, Zbl 0712.35001 .

books.google.com

See the commentary of Peter Lax to the paper (Friedrichs 1944) in (Friedrichs 1986, volume 1, p. 117). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced. Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S., 편집., 《Selecta》, Contemporary Mathematicians, Boston-Basel-Stuttgart: Birkhäuser Verlag, 427 (Vol. 1); pp. 608 (Vol. 2)쪽, ISBN 0-8176-3270-0, Zbl 0613.01020 . A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgag Wasow, Harold Weitzner.
Lax (Friedrichs 1986, volume 1, p. 117) writes precisely that:-"On English usage Friedrichs liked to consult his friend and colleague, Donald Flanders, a descendant of puritans and a puritan himself, with the highest standard of his own conduct, noncensorious towards others. Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S., 편집., 《Selecta》, Contemporary Mathematicians, Boston-Basel-Stuttgart: Birkhäuser Verlag, 427 (Vol. 1); pp. 608 (Vol. 2)쪽, ISBN 0-8176-3270-0, Zbl 0613.01020 . A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgag Wasow, Harold Weitzner.
See (Giusti 1984, 11쪽). Giusti, Enrico (1984), 《Minimal surfaces and functions of bounded variations》, Monographs in Mathematics 80, Basel-Boston-Stuttgart: Birkhäuser Verlag, xii+240쪽, ISBN 0-8176-3153-4, MR 0775682, Zbl 0545.49018 .

doi.org

dx.doi.org

See (Friedrichs 1944, 136–139쪽). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See the commentary of Peter Lax to the paper (Friedrichs 1944) in (Friedrichs 1986, volume 1, p. 117). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced. Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S., 편집., 《Selecta》, Contemporary Mathematicians, Boston-Basel-Stuttgart: Birkhäuser Verlag, 427 (Vol. 1); pp. 608 (Vol. 2)쪽, ISBN 0-8176-3270-0, Zbl 0613.01020 . A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgag Wasow, Harold Weitzner.
As when the paper (Friedrichs 1944) was published, few years before Laurent Schwartz widespread his work. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Friedrichs 1944, 136–138쪽), properties PI, PII, PIII and their consequence PIII₀. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
Also, in this respect, Friedrichs (1944, 132쪽) says:-"The main tool for the proof is a certain class of smoothing operators approximating unity, the "mollifiers". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Friedrichs 1944, 137쪽), paragraph 2, "Integral operators". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.

jstor.org

See (Friedrichs 1944, 136–139쪽). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See the commentary of Peter Lax to the paper (Friedrichs 1944) in (Friedrichs 1986, volume 1, p. 117). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced. Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S., 편집., 《Selecta》, Contemporary Mathematicians, Boston-Basel-Stuttgart: Birkhäuser Verlag, 427 (Vol. 1); pp. 608 (Vol. 2)쪽, ISBN 0-8176-3270-0, Zbl 0613.01020 . A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgag Wasow, Harold Weitzner.
As when the paper (Friedrichs 1944) was published, few years before Laurent Schwartz widespread his work. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Friedrichs 1944, 136–138쪽), properties PI, PII, PIII and their consequence PIII₀. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
Also, in this respect, Friedrichs (1944, 132쪽) says:-"The main tool for the proof is a certain class of smoothing operators approximating unity, the "mollifiers". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Friedrichs 1944, 137쪽), paragraph 2, "Integral operators". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.

mathnet.ru

mi.mathnet.ru

See (Sobolev 1938). Sobolev, Sergei L. (1938), “Sur un théorème d'analyse fonctionnelle”, 《Recueil Mathématique (Matematicheskii Sbornik)》 (러시아어프랑스어), 4(46) (3): 471–497, Zbl 0022.14803 . The paper where Sergei Sobolev proved his embedding theorem, introducing and using integral operators very similar to mollifiers, without naming them.

wikipedia.org

en.wikipedia.org

Respect to the topology of the given space of generalized functions.
See (Friedrichs 1944, 136–139쪽). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See the commentary of Peter Lax to the paper (Friedrichs 1944) in (Friedrichs 1986, volume 1, p. 117). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced. Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S., 편집., 《Selecta》, Contemporary Mathematicians, Boston-Basel-Stuttgart: Birkhäuser Verlag, 427 (Vol. 1); pp. 608 (Vol. 2)쪽, ISBN 0-8176-3270-0, Zbl 0613.01020 . A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgag Wasow, Harold Weitzner.
Lax (Friedrichs 1986, volume 1, p. 117) writes precisely that:-"On English usage Friedrichs liked to consult his friend and colleague, Donald Flanders, a descendant of puritans and a puritan himself, with the highest standard of his own conduct, noncensorious towards others. Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S., 편집., 《Selecta》, Contemporary Mathematicians, Boston-Basel-Stuttgart: Birkhäuser Verlag, 427 (Vol. 1); pp. 608 (Vol. 2)쪽, ISBN 0-8176-3270-0, Zbl 0613.01020 . A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgag Wasow, Harold Weitzner.
See (Sobolev 1938). Sobolev, Sergei L. (1938), “Sur un théorème d'analyse fonctionnelle”, 《Recueil Mathématique (Matematicheskii Sbornik)》 (러시아어프랑스어), 4(46) (3): 471–497, Zbl 0022.14803 . The paper where Sergei Sobolev proved his embedding theorem, introducing and using integral operators very similar to mollifiers, without naming them.
Such as a bump function
See (Giusti 1984, 11쪽). Giusti, Enrico (1984), 《Minimal surfaces and functions of bounded variations》, Monographs in Mathematics 80, Basel-Boston-Stuttgart: Birkhäuser Verlag, xii+240쪽, ISBN 0-8176-3153-4, MR 0775682, Zbl 0545.49018 .
As when the paper (Friedrichs 1944) was published, few years before Laurent Schwartz widespread his work. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
Obviously the topology with respect to convergence occurs is the one of the Hilbert or Banach space considered.
See (Friedrichs 1944, 136–138쪽), properties PI, PII, PIII and their consequence PIII₀. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
Also, in this respect, Friedrichs (1944, 132쪽) says:-"The main tool for the proof is a certain class of smoothing operators approximating unity, the "mollifiers". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Friedrichs 1944, 137쪽), paragraph 2, "Integral operators". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Hörmander 1990, 14쪽), lemma 1.2.3.: the example is stated in implicit form by first defining $f (t) = exp(-1/ t)$ for $t$ ∈ ℝ⁺, and then considering $f (x) = f (1-| x | 2) = exp(-1/(1-| x | 2))$ for $x$ ∈ ℝⁿ. Hörmander, Lars (1990), 《The analysis of linear partial differential operators I》, Grundlehren der Mathematischen Wissenschaft 256 2판, Berlin-Heidelberg-New York: Springer-Verlag, ISBN 0-387-52343-X, MR 1065136, Zbl 0712.35001 .
See for example (Hörmander 1990). Hörmander, Lars (1990), 《The analysis of linear partial differential operators I》, Grundlehren der Mathematischen Wissenschaft 256 2판, Berlin-Heidelberg-New York: Springer-Verlag, ISBN 0-387-52343-X, MR 1065136, Zbl 0712.35001 .
A proof of this fact can be found in (Hörmander 1990, 25쪽), Theorem 1.4.1. Hörmander, Lars (1990), 《The analysis of linear partial differential operators I》, Grundlehren der Mathematischen Wissenschaft 256 2판, Berlin-Heidelberg-New York: Springer-Verlag, ISBN 0-387-52343-X, MR 1065136, Zbl 0712.35001 .

zbmath.org

See (Friedrichs 1944, 136–139쪽). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See the commentary of Peter Lax to the paper (Friedrichs 1944) in (Friedrichs 1986, volume 1, p. 117). Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced. Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S., 편집., 《Selecta》, Contemporary Mathematicians, Boston-Basel-Stuttgart: Birkhäuser Verlag, 427 (Vol. 1); pp. 608 (Vol. 2)쪽, ISBN 0-8176-3270-0, Zbl 0613.01020 . A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgag Wasow, Harold Weitzner.
Lax (Friedrichs 1986, volume 1, p. 117) writes precisely that:-"On English usage Friedrichs liked to consult his friend and colleague, Donald Flanders, a descendant of puritans and a puritan himself, with the highest standard of his own conduct, noncensorious towards others. Friedrichs, Kurt Otto (1986), Morawetz, Cathleen S., 편집., 《Selecta》, Contemporary Mathematicians, Boston-Basel-Stuttgart: Birkhäuser Verlag, 427 (Vol. 1); pp. 608 (Vol. 2)쪽, ISBN 0-8176-3270-0, Zbl 0613.01020 . A selection from Friedrichs' works with a biography and commentaries of David Isaacson, Fritz John, Tosio Kato, Peter Lax, Louis Nirenberg, Wolfgag Wasow, Harold Weitzner.
See (Sobolev 1938). Sobolev, Sergei L. (1938), “Sur un théorème d'analyse fonctionnelle”, 《Recueil Mathématique (Matematicheskii Sbornik)》 (러시아어프랑스어), 4(46) (3): 471–497, Zbl 0022.14803 . The paper where Sergei Sobolev proved his embedding theorem, introducing and using integral operators very similar to mollifiers, without naming them.
See (Giusti 1984, 11쪽). Giusti, Enrico (1984), 《Minimal surfaces and functions of bounded variations》, Monographs in Mathematics 80, Basel-Boston-Stuttgart: Birkhäuser Verlag, xii+240쪽, ISBN 0-8176-3153-4, MR 0775682, Zbl 0545.49018 .
As when the paper (Friedrichs 1944) was published, few years before Laurent Schwartz widespread his work. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Friedrichs 1944, 136–138쪽), properties PI, PII, PIII and their consequence PIII₀. Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
Also, in this respect, Friedrichs (1944, 132쪽) says:-"The main tool for the proof is a certain class of smoothing operators approximating unity, the "mollifiers". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Friedrichs 1944, 137쪽), paragraph 2, "Integral operators". Friedrichs, Kurt Otto (January 1944), “The identity of weak and strong extensions of differential operators”, 《Transactions of the American Mathematical Society》 55 (1): 132–151, doi:10.1090/S0002-9947-1944-0009701-0, JSTOR 1990143, MR 0009701, Zbl 0061.26201 . The first paper where mollifiers were introduced.
See (Hörmander 1990, 14쪽), lemma 1.2.3.: the example is stated in implicit form by first defining $f (t) = exp(-1/ t)$ for $t$ ∈ ℝ⁺, and then considering $f (x) = f (1-| x | 2) = exp(-1/(1-| x | 2))$ for $x$ ∈ ℝⁿ. Hörmander, Lars (1990), 《The analysis of linear partial differential operators I》, Grundlehren der Mathematischen Wissenschaft 256 2판, Berlin-Heidelberg-New York: Springer-Verlag, ISBN 0-387-52343-X, MR 1065136, Zbl 0712.35001 .
See for example (Hörmander 1990). Hörmander, Lars (1990), 《The analysis of linear partial differential operators I》, Grundlehren der Mathematischen Wissenschaft 256 2판, Berlin-Heidelberg-New York: Springer-Verlag, ISBN 0-387-52343-X, MR 1065136, Zbl 0712.35001 .
A proof of this fact can be found in (Hörmander 1990, 25쪽), Theorem 1.4.1. Hörmander, Lars (1990), 《The analysis of linear partial differential operators I》, Grundlehren der Mathematischen Wissenschaft 256 2판, Berlin-Heidelberg-New York: Springer-Verlag, ISBN 0-387-52343-X, MR 1065136, Zbl 0712.35001 .