Skip to content
DraconiticResearch
Search Sources API
188,932 studies31 sourcesUpdated 5 min ago
PreprintarXiv licencearXiv

Fourier analysis on a class of Schwartz spaces and applications

  • Isadora Vieira Coelho da Silva
  • Paulo Leandro Dattori da Silva
  • Michael Ruzhansky
Open at sourcePDFDOICite

Abstract

The study of regularity and solvability of partial differential operators on non-compact manifolds requires the construction of adapted functional spaces. In this work we introduce ๐’ฎ(Mร—โ„n), the Schwartz space on the product of a homogeneous space M and the Euclidean space โ„n. We characterize ๐’ฎ(Mร—โ„n) and its topological dual by employing discrete Fourier analysis in terms of eigenfunction expansions associated with a class of anisotropic elliptic operators on โ„n. We provide a characterization via partial Fourier coefficients and via full coefficients, that is, with respect to both components of M ร— โ„n simultaneously, which is achieved by studying the Fourier analysis on M. Our results provide new tools for the analysis of operators in this broader setting. As an application, we investigate the global existence and regularity of solutions for a class of partial differential equations on Mร— โ„n.

Related

  1. Schwartz-Class Gabor Windows and the Balian-Low Classification
    Andrei Caragea, Gรถtz Pfander
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  2. A class of ฮจ-bounded oscillation operators on abstract Orlicz-Morrey spaces endowed with a ball-basis and their applications
    F. Shan, J. Zhou
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  3. Commutators of a class of ฮจ-bounded oscillation operators on abstract weighted Orlicz-Morrey spaces endowed with ball-basis and applications
    Fate Shan, Wei Wang, Yuchen Li +1
    arXivPreprintarXiv licenceFull textAnalysis & PDEsarXiv
  4. Chern-Schwartz-MacPherson classes of symmetric powers and applications
    Barbara Fantechi, Lothar Goettsche
    arXivPreprintCC BY-NC-ND 4.0Full textAlgebra & number theoryarXiv
  5. Birational maps of moduli spaces of stable sheaves on a K3 surface induced by Fourier-Mukai transforms
    Kota Yoshioka
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryarXiv

Cite

BibTeXRIS
BibTeX
@misc{silva2026fourier,
  title = {{Fourier analysis on a class of Schwartz spaces and applications}},
  author = {Isadora Vieira Coelho da Silva and Paulo Leandro Dattori da Silva and Michael Ruzhansky},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.00302},
  eprint = {2611.00302},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.00302},
}
RIS
TY  - UNPB
TI  - Fourier analysis on a class of Schwartz spaces and applications
AU  - Isadora Vieira Coelho da Silva
AU  - Paulo Leandro Dattori da Silva
AU  - Michael Ruzhansky
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.00302
UR  - https://arxiv.org/abs/2611.00302
AB  - The study of regularity and solvability of partial differential operators on non-compact manifolds requires the construction of adapted functional spaces. In this work we introduce ๐’ฎ(Mร—โ„^n), the Schwartz space on the product of a homogeneous space M and the Euclidean space โ„^n. We characterize ๐’ฎ(Mร—โ„^n) and its topological dual by employing discrete Fourier analysis in terms of eigenfunction expansions associated with a class of anisotropic elliptic operators on โ„^n. We provide a characterization via partial Fourier coefficients and via full coefficients, that is, with respect to both components of M ร— โ„^n simultaneously, which is achieved by studying the Fourier analysis on M. Our results provide new tools for the analysis of operators in this broader setting. As an application, we investigate the global existence and regularity of solutions for a class of partial differential equations on Mร— โ„^n.
ER  -