Work

Stability of shifts, interpolation, and spectrum of atomic measures

Year: 2025

Type: article

Abstract: We ask which functions and separated sets have the property that the ‐shifts of form an unconditional basis in the ‐closure of their span for every . The main result establishes the equivalence of this property to each of the two seemingly unrelated conditions: is a set of interpolation for certain Paley–Wiener spaces and the nonexistence of certain measures with given support and spectrum. As a consequence, we answer the question for wide classes of functions and sets . In particular, we show the connection between the property and the nonexistence of certain crystalline measures.

Source: Journal of the London Mathematical Society

DOI: 10.1112/jlms.70267

Authors: Alexander Ulanovskii, Ilya Zlotnikov

Institutions: University of Stavanger, University of Vienna, Norwegian University of Science and Technology

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funders: Austrian Science Fund, Norges Forskningsråd