Titlebook: Integral Operators in the Theory of Linear Partial Differential Equations; Stefan Bergman Book 1969 Springer-Verlag Berlin Heidelberg 1969

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978-3-662-37293-7Springer-Verlag Berlin Heidelberg 1969

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Introduction,In the following we shall explain the basic ideas of the theory of integral operators generating solutions of linear partial differential equations with analytic coefficients.

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Ergebnisse der Mathematik und Ihrer Grenzgebiete. 1. Folgehttp://image.papertrans.cn/i/image/468334.jpg

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Differential equations in two variables with entire coefficients,so-called integral operator of the first kind which will be discussed in §§ 1–3. We shall express solutions . in terms of an arbitrary function of a complex variable .(.). Next, .(.) will be expressed in terms of a function .(.) which essentially coincides with .(., 0), see (2. 1) and (2–5).

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Harmonic functions in three variables, functions represent a linear space, but they neither form an algebra nor possess group properties. However, by associating, in a one-to-one way, a function .. of one or more complex variables with every hormonic function of three variables, .. = ..(..), . = 1, 2, we can define a composition rule “ʘ” for the .. by writing

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