Sequences of generalized moments and their applications to some moment partial differential equations
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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BibTeX
@misc{michalik2026sequences,
title = {{Sequences of generalized moments and their applications to some moment partial differential equations}},
author = {Sławomir Michalik and Hiroshi Yamazawa},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37138},
eprint = {2609.37138},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37138},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Sequences of generalized moments and their applications to some moment partial differential equations
AU - Sławomir Michalik
AU - Hiroshi Yamazawa
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37138
UR - https://arxiv.org/abs/2609.37138
AB - 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.
ER -