Remarques diverses sur l'équation de Fredholm
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This article is published in Acta Mathematica.The article was published on 1910-12-01 and is currently open access. It has received 20 citations till now.read more
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Notes on infinite determinants of Hilbert space operators
TL;DR: In this article, the basic facts about determinants and traces of trace class operators on a separable Hilbert space are presented, including Lidskii's theorem on the equality of the matrix and spectral traces.
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Hilbert-Carleman and regularized determinants for linear operators
TL;DR: In this article, a general theory of regularized and Hilbert-Carleman determinants in normed algebras of operators acting in Banach spaces is proposed, where regularized determinants are defined as continuous extensions of the corresponding determinants of finite dimensional operators.
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Toeplitz matrices and operators
TL;DR: The theory of Toeplitz matrices and operators is a vital part of modern analysis, with applications to moment problems, orthogonal polynomials, approximation theory, integral equations, bounded-and vanishing-mean oscillations, and asymptotic methods for large structured determinants, among others.
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An Overview of Complex Fractal Dimensions: From Fractal Strings to Fractal Drums, and Back
TL;DR: The theory of complex fractal dimensions and their associated geometric or fractal zeta functions is discussed in this article. But the main goal of this article is to provide an overview of the theory of these dimensions.
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Measures on Banach manifolds and supersymmetric quantum field theory
TL;DR: In this article, the authors show how to construct Borel probability measures on Banach manifolds associated to supersymmetric quantum field theories, which are mathematically well defined objects inspired by the formal path integrals appearing in the physics literature on quantum field theory.