THE EQUATION (I-S)g=/ FOR SHIFT OPERATORS IN HILBERT SPACE
نویسنده
چکیده
Kac's method is to find formally the Fourier coefficients of g in (2), use the Holder condition on/ and the condition (1) to estimate the size of these coefficients and show that they are, in fact, the Fourier coefficients of a function in 72(0, 1). Z. Ciesielski has since extended the theorem to the case a>0 [l]. The basic difference between Ciesielski's approach and Kac's is the use of Fourier-Haar coefficients in place of Fourier coefficients. It will be the purpose of this paper to prove a theorem about inverting certain operators on Hilbert space. Theorem 1 will then be shown to be an immediate consequence of our more general theorem. First however, we introduce some definitions and established results.
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تاریخ انتشار 2010