Bergman operators for parabolic equations in two space variables

Colton, David

doi:10.1090/S0002-9939-1973-0312054-5

Bergman operators for parabolic equations in two space variables
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Proc. Amer. Math. Soc. 38 (1973), 119-126 Request permission

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.

References

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