Integral Operators in the Theory of Linear Partial Differential Equations

1962 ◽  
Vol 46 (357) ◽  
pp. 256
Author(s):  
E. T. Copson ◽  
Stefan Bergman
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Operators ◽  
Partial Differential ◽  
Linear Partial Differential Equations

Bounds for Solutions of a System of Linear Partial Differential Equations on Domains with Bergman-Silov Boundary

1966 ◽  
Vol 18 ◽  
pp. 1272-1280
Author(s):  
Josephine Mitchell
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Entire Functions ◽  
Integral Operators ◽  
Holomorphic Functions ◽  
Complex Variables ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Systems Of Differential Equations ◽  
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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 system1where z1, z1*, z2, z2* are independent complex variables and the functions Fj (J = 1, 2) are entire functions of the indicated variables.

Construction of kernels of integral operators for linear partial differential equations

1980 ◽  
Vol 10 (4) ◽  
pp. 261-273 ◽  
Author(s):  
Ali Azzam ◽  
Erwin Kreyszig ◽  
R. P. Gilbert ◽  
K. W. Bauer ◽  
K. Ecker ◽  
...  
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Integral Operators ◽  
Partial Differential ◽  
Linear Partial Differential Equations
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