Work

Pseudodifferential operators on time-frequency shift invariant ultradistributions with periodic symbols

Year: 2026

Type: article

Abstract: In the present paper the authors study pseudodifferential operators with periodic symbols acting on time-frequency shift invariant spaces of generalized ultradistributions. Particular attention is devoted to symbols satisfying suitable Gelfand–Shilov type regularity conditions, which exhibit periodicity with respect to appropriate lattice structures. In this framework, we show how periodicity allows us to represent the corresponding operators in terms of time-frequency shifts. We then establish continuity and invertibility results on a broad class of Banach spaces of ultradistributions, extending previous results known in the tempered distribution setting. The analysis provides a natural functional framework for treating non-polynomial weights, including weights with exponential growth at infinity.

Source: ANNALI DELL UNIVERSITA DI FERRARA

DOI: 10.1007/s11565-026-00740-2

Authors: Gianluca Garello, Alessandro Morando

Institutions: University of Turin, Istituto Nazionale di Alta Matematica Francesco Severi, University of Brescia

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Università degli Studi di Torino, Ministero dell'Università e della Ricerca