The identity of weak and strong extensions of differential operators

Author:
K. O. Friedrichs

Journal:
Trans. Amer. Math. Soc. **55** (1944), 132-151

MSC:
Primary 46.3X

DOI:
https://doi.org/10.1090/S0002-9947-1944-0009701-0

MathSciNet review:
0009701

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References | Similar Articles | Additional Information

**[1]**Kurt Friedrichs,*On Differential Operators in Hilbert Spaces*, Amer. J. Math.**61**(1939), no. 2, 523–544. MR**1507392**, https://doi.org/10.2307/2371518**[2]**-,*On hyperbolic differential operators*, Bull. Amer. Math. Soc. Abstract 46-9-416 (1940) p. 754.**[3]**M. Bôcher,*On harmonic functions in two dimensions*, Proceedings of the American Academy of Sciences vol. 41 (1905-1906).**[4]**Griffith C. Evans,*On the reduction of integro-differential equations*, Trans. Amer. Math. Soc.**15**(1914), no. 4, 477–496. MR**1500991**, https://doi.org/10.1090/S0002-9947-1914-1500991-2**[5]**-,*Fundamental points of potential theory*, Rice Institute Pamphlets vol. 7 (1920) p. 274.*Complements of potential theory*. I, Amer. J. Math. vol. 55 (1933) p. 42.**[6]**C. B. Morrey, Jr.,*A class of representations of manifolds*. I, Amer. J. Math. vol. 55 (1933) p. 687.**[7]**J. W. Calkin,*Functions of several variables and absolute continuity. I*, Duke Math. J.**6**(1940), 170–186. MR**1278****[8]**Norbert Wiener,*The operational calculus*, Math. Ann.**95**(1926), no. 1, 557–584. MR**1512294**, https://doi.org/10.1007/BF01206627**[9]**R. Courant and D. Hilbert,*Methoden der mathematischen Physik*, vol. 2, p. 470.**[10]**D. C. Lewis,*Infinite systems of ordinary differential equations*, Trans. Amer. Math. Soc. vol. 35 (1933) p. 808.**[11]**Hermann Weyl,*The method of orthogonal projection in potential theory*, Duke Math. J.**7**(1940), 411–444. MR**3331****[12]**K. Ogura, Tôhoku Math. J. vol. 16 (1919).**[13]**J. von Neumann,*Über adjungierte Funktionaloperatoren*, Ann. of Math. vol. 33 (1932) p. 294.**[14]**C. B. Morrey Jr.,*Functions of several variables and absolute continuity, II*, Duke Math. J.**6**(1940), 187–215. MR**1279****[15]**-,*On the solutions of quasilinear elliptic partial differential equations*, Trans. Amer. Math. Soc. vol. 43 (1938) p. 126.*Existence and differentiability theorems for the solutions of variational problems for multiple integrals*, Bull. Amer. Math. Soc. vol. 46 (1940) p. 439.

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DOI:
https://doi.org/10.1090/S0002-9947-1944-0009701-0

Article copyright:
© Copyright 1944
American Mathematical Society