Isomorphism problem and averaging for nondifferential operators

I. O. Gushchin, S. V. Kislyakov

St. Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: The methods and results of a recent paper by the authors (Algebra i Analiz, 37, No. 4, 2025, pp. 166-180) are transferred to analogs of spaces of smooth functions generated by a certain class of Fourier multipliers. Unlike differential operators, multipliers are often nonlocal.

Key words and phrases: Fourier multiplier, Poisson summation formula, complemented subspace.

UDC: 517

Received: 01.12.2025