TY - JOUR
AU - Borichev, A. A.
AB - We investigate primary ideals at ∞ in Beurling‐type Frechet algebras in the quasianalytic case. They are described by two parameters characterizing the rate of decay of their Fourier transforms at ±∞ (Theorem 9.6). We use the so‐called generalized Fourier transform to treat related convolution equations. A necessary and sufficient condition for the orthogonality of a functional with empty spectrum and an ideal generated by a function is given in terms of their Fourier transforms (Theorem 3.6). Furthermore, we describe all primary ideals at ∞ in Beurling‐type algebras on the half‐line (Theorem 9.7).
TI - Beurling Algebras and the Generalized Fourier Transform
JF - Proceedings of the London Mathematical Society
DO - 10.1112/plms/s3-73.2.431
DA - 1996-09-01
UR - https://www.deepdyve.com/lp/wiley/beurling-algebras-and-the-generalized-fourier-transform-FD1fkvPI9n
SP - 431
EP - 480
VL - s3-73
IS - 2
DP - DeepDyve
ER -