TY - JOUR

T1 - HARMONIC ANALYSIS ON THE SPACE OF M‑POSITIVE VECTORS

AU - Farkov, Yu.

AU - Скопина, Мария Александровна

PY - 2023/8/26

Y1 - 2023/8/26

N2 - Given a dilation matrix M, a so-called space of M-positive vectors in the Euclidean space is introduced and studied. An algebraic structure of this space is similar to the positive half-line equipped with the termwise addition modulo 2, which is used in the Walsh analysis. The role of harmonics is played by some analogues of the classical Walsh functions. The concept of Fourier transform is introduced, and the Poisson summation formula, Plancherel theorem, Vilenkin-Chrestenson formulas and so on are proved. A kind of analogue of the Schwartz class is studied. This class consists of functions such that both the function itself and its Fourier transform have compact support.

AB - Given a dilation matrix M, a so-called space of M-positive vectors in the Euclidean space is introduced and studied. An algebraic structure of this space is similar to the positive half-line equipped with the termwise addition modulo 2, which is used in the Walsh analysis. The role of harmonics is played by some analogues of the classical Walsh functions. The concept of Fourier transform is introduced, and the Poisson summation formula, Plancherel theorem, Vilenkin-Chrestenson formulas and so on are proved. A kind of analogue of the Schwartz class is studied. This class consists of functions such that both the function itself and its Fourier transform have compact support.

KW - Characters

KW - Fourier transform

KW - Fractal sets

KW - Space of M-positive vectors

KW - Step-functions

KW - Walsh functions

UR - https://www.mendeley.com/catalogue/0958b740-4bc6-3e8c-a801-85faddc45766/

U2 - 10.1007/s10958-023-06601-z

DO - 10.1007/s10958-023-06601-z

M3 - Article

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

ER -