A handy formula for the Fredholm index of Toeplitz plus Hankel operators
نویسندگان
چکیده
منابع مشابه
A Fredholm determinant formula for Toeplitz determinants
as the Fredholm determinant of an operator 1−K acting on l2({n, n+1, . . . }), where the kernel K = K(φ) admits an integral representation in terms of φ. The answer is affirmative and the construction of the kernel is explained below. We give two versions of the result: an algebraic one, which holds in the suitable algebra of formal power series, and an analytic one. In order to minimize the am...
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In many applications, e.g. digital signal processing, discrete inverse scattering, linear prediction etc., Toeplitz-plus-Hankel (T + H) matrices need to be inverted. (For further applications see [1] and references therein). Firstly the T +H matrix inversion problem has been solved in [2] where it was reduced to the inversion problem of the block Toeplitz matrix (the so-called mosaic matrix). T...
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We study the boundedness properties of truncation operators acting on bounded Hankel (or Toeplitz) infinite matrices. A relation with the Lacey-Thiele theorem on the bilinear Hilbert transform is established. We also study the behaviour of the truncation operators when restricted to Hankel matrices in the Schatten classes. 1. Statement of results In this note we will be dealing with infinite ma...
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We characterize when a Hankel operator and a Toeplitz operator have a compact commutator. Let dσ(w) be the normalized Lebesgue measure on the unit circle ∂D. The Hardy space H is the subspace of L(∂D, dσ), denoted by L, which is spanned by the space of analytic polynomials. So there is an orthogonal projection P from L onto the Hardy space H, the so-called Hardy projection. Let f be in L∞. The ...
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The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the method.
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ژورنال
عنوان ژورنال: Indagationes Mathematicae
سال: 2012
ISSN: 0019-3577
DOI: 10.1016/j.indag.2012.06.008