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On weights which admit harmonic Bergman kernel and minimal solutions of Laplace's equation (Q2081361)

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scientific article; zbMATH DE number 7600494
Language Label Description Also known as
English
On weights which admit harmonic Bergman kernel and minimal solutions of Laplace's equation
scientific article; zbMATH DE number 7600494

    Statements

    title
    On weights which admit harmonic Bergman kernel and minimal solutions of Laplace's equation (English)
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    publication date
    12 October 2022
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    review text
    The paper deals with weighted spaces of harmonic functions on a bounded domain of square summable functions with some measure (weight). For such spaces, more precisely for weights, the question of the existence of a reproducing kernel is considered. Conditions are given in terms of the integrability of the weight to a negative power (not exceeding \(-1\)). Some illustrating examples are given as well.
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    zbMATH Keywords
    harmonic Bergman kernel
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    reproducing kernel Hilbert space
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    weight of integration
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    admissible weight
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    functional of point evaluation
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    Laplace equation
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    minimal solution
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    Identifiers

    zbMATH DE Number
    7600494
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    OpenAlex ID
    W4296045795
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