L 2 (R) Solutions of Dilation Equations and Fourier-Like Transforms
نویسندگان
چکیده
منابع مشابه
Positive-definiteness, Integral Equations and Fourier Transforms
We show that positive definite kernel functions k(x, y), if continuous and integrable along the main diagonal, coincide with kernels of positive integral operators in L2(R). Such an operator is shown to be compact; under the further assumption k(x, x) → 0 as |x| → ∞ it is also trace class and the corresponding bilinear series converges absolutely and uniformly. If k1/2(x, x) ∈ L1(R), all these ...
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ژورنال
عنوان ژورنال: Journal of Fourier Analysis and Applications
سال: 2002
ISSN: 1069-5869,1531-5851
DOI: 10.1007/s00041-002-0015-4