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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Bergman operators for parabolic equations in two space variables


Author: David Colton
Journal: Proc. Amer. Math. Soc. 38 (1973), 119-126
MSC: Primary 35C15
MathSciNet review: 0312054
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Abstract: An integral operator is constructed which maps analytic functions of two complex variables onto the class of real valued analytic solutions of linear second order parabolic equations in two space variables with real valued, analytic, time independent coefficients. When the solution of the parabolic equation is independent of the time variable the operator reduces to Bergman's integral operator for elliptic equations in two independent variables.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0312054-5
Keywords: Integral operator, Bergman operator, parabolic equation, elliptic equation, Goursat data, analytic function
Article copyright: © Copyright 1973 American Mathematical Society