Bounded symbols of Toeplitz operators on Paley-Wiener spaces and a weak factorization theorem

2025/10/01 by P. A. Kulikov, Kulikov, Petr
Mathematics · #Holomorphic and Operator Theory #Algebraic and Geometric Analysis #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2510.01374

Abstract

A classical result by R. Rochberg says that every bounded Toeplitz operator T on the Hilbert Paley-Wiener space PW_a² admits a bounded symbol φ. We generalize this result to Toeplitz operators on the Banach Paley-Wiener spaces PW_a^p, 11, (1)/(p)+(1)/(q)=1, any function h belonging to PW¹_2a can be represented as h=∑_{k\geqslant 0}f_kg_k, f_k\inPW_a^p, g_k\inPW_a^q.

Citations

• Bounded symbols and reproducing kernel thesis for truncated Toeplitz operators

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