Geodesic
Bounds for Solutions of a System of Linear Partial Differential Equations on Domains with Bergman-Silov Boundary
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1272-1280

Voir la notice de l'article provenant de la source Cambridge University Press

The method of integral operators has been used by Bergman and others (4; 6; 7; 10; 12) to obtain many properties of solutions of linear partial differential equations. In the case of equations in two variables with entire coefficients various integral operators have been introduced which transform holomorphic functions of one complex variable into solutions of the equation. This approach has been extended to differential equations in more variables and systems of differential equations. Recently Bergman (6; 4) obtained an integral operator transforming certain combinations of holomorphic functions of two complex variables into functions of four real variables which are the real parts of solutions of the system 1 where z1, z1*, z2, z2* are independent complex variables and the functions Fj (J = 1, 2) are entire functions of the indicated variables. 
Mitchell, Josephine. Bounds for Solutions of a System of Linear Partial Differential Equations on Domains with Bergman-Silov Boundary. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 1272-1280. doi: 10.4153/CJM-1966-126-8
@article{10_4153_CJM_1966_126_8,
     author = {Mitchell, Josephine},
     title = {Bounds for {Solutions} of a {System} of {Linear} {Partial} {Differential} {Equations} on {Domains} with {Bergman-Silov} {Boundary}},
     journal = {Canadian journal of mathematics},
     pages = {1272--1280},
     year = {1966},
     volume = {18},
     number = {1},
     doi = {10.4153/CJM-1966-126-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-126-8/}
}
TY  - JOUR
AU  - Mitchell, Josephine
TI  - Bounds for Solutions of a System of Linear Partial Differential Equations on Domains with Bergman-Silov Boundary
JO  - Canadian journal of mathematics
PY  - 1966
SP  - 1272
EP  - 1280
VL  - 18
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-126-8/
DO  - 10.4153/CJM-1966-126-8
ID  - 10_4153_CJM_1966_126_8
ER  - 
%0 Journal Article
%A Mitchell, Josephine
%T Bounds for Solutions of a System of Linear Partial Differential Equations on Domains with Bergman-Silov Boundary
%J Canadian journal of mathematics
%D 1966
%P 1272-1280
%V 18
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1966-126-8/
%R 10.4153/CJM-1966-126-8
%F 10_4153_CJM_1966_126_8

[1] 1. Ahlfors, L. V., An extension of Schwarz's lemma, Trans. Amer. Math. Soc., 43 (1938), 359–364. Google Scholar

[2] 2. Bergman, S., Über eine in gewissen Bereichen gilltige Integraldarstellung der Funktionen zweier komplexer Variablen, Math. Z., 89 (1934), 76–94, 605-608. Google Scholar

[3] 3. Bergman, S., Bounds for analytic functions in domains with a distinguished boundary surface, Math. Z., 63 (1955), 173–194. Google Scholar

[4] 4. Bergman, S., Bounds for solutions of a system of partial differential equations, J. Rational Mech. and Anal., 5, (1956), 993–1002. Google Scholar

[5] 5. Bergman, S., Sur les fonctions orthogonales de plusieurs variables complexes (Paris, 1947). Google Scholar

[6] 6. Bergman, S., Integral operators in the theory of linear partial differential equations (Berlin, 1961). Google Scholar

[7] 7. Bergman, S. and Schiffer, M., Properties of solutions of a system of partial differential equations, Studies in Math, and Mech. presented to Richard von Mises (New York, 1954), 79–87. Google Scholar

[8] 8. Carathéodory, C., Conformai representation (Cambridge, 1941). Google Scholar

[9] 9. Charyński, Z., Bounds for analytic functions of two complex variables, Math. Z., 75 (1961), 29–35. Google Scholar

[10] 10. Gilbert, R. P., Some properties of generalized axially symmetric potentials, Amer. J. Math., 84 (1962), 475–484. Google Scholar

[11] 11. Kelley, J. L., General topology (Princeton, N.J., 1955). Google Scholar

[12] 12. Mitchell, J., Properties of harmonic functions of 3 real variables given by Bergman-Whittaker operators, Can. J. Math., 15 (1963), 157–168. Google Scholar

[13] 13. Śladkowska, J., Bounds of analytic functions of two complex variables in domains with the Bergman-Silov boundary, Pacific J. Math., 12 (1962), 1435–1451. Google Scholar

Cité par Sources :