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arXiv · 2609.37138

Sequences of generalized moments and their applications to some moment partial differential equations

Sławomir Michalik·Hiroshi Yamazawa
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Abstract

We introduce sequences of generalized moments that are a generalization of sequences preserving summability and sequences of moments from Balser's theory of moment summability. We construct extensions of Laplace and Borel integral operators for these new sequences. We find integral representations of moment derivatives for generalized moments. We show the characterization of summable solutions of moment-PDEs with generalized moments. We describe singular directions for summable solutions of moment-PDEs with generalized moments and we express jumps across these singular directions in terms of hyperfunctions and in terms of kernel functions associated with sequences preserving summability, which are connected with given sequences of generalized moments.

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Sławomir Michalik, Hiroshi Yamazawa. 2026-09-29. Sequences of generalized moments and their applications to some moment partial differential equations. https://arxiv.org/abs/2609.37138

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