<i>Analytic Function Theory, Volume 2</i>

Hille, Einar; Weiss, Guido

doi:10.1063/1.3057867

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Introduction2

Rational Eigenfunctions1

Functions Holomorphic In a Half-plane1

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Cited by 163 publications

(170 citation statements)

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“…The notion of logarithmic capacity is introduced in the framework of potential theory; see e.g. [7,11]. Recall that the logarithmic capacity of compact sets in R 2 has the following properties:…”

Section: Introductionmentioning

confidence: 99%

Spectral Asymptotics of Pauli Operators and Orthogonal Polynomials in Complex Domains

Filonov

Pushnitski

2006

Commun. Math. Phys.

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We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation of eigenvalues to zero is described in terms of the logarithmic capacity of the support of the electric potential. A connection between these eigenvalues and orthogonal polynomials in complex domains is established.

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Section: Introductionmentioning

confidence: 99%

Spectral Asymptotics of Pauli Operators and Orthogonal Polynomials in Complex Domains

Filonov

Pushnitski

2006

Commun. Math. Phys.

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“…Further theoretical properties of these functions are discussed in [6], [12, §2.6.4], and [13,Ch. 19].…”

Section: Rational Eigenfunctionsmentioning

confidence: 99%

Computing the Hilbert Transform on the Real Line

Weideman¹

1995

Mathematics of Computation

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Abstract. We introduce a new method for computing the Hubert transform on the real line. It is a collocation method, based on an expansion in rational eigenfunctions of the Hubert transform operator, and implemented through the Fast Fourier Transform. An error analysis is given, and convergence rates for some simple classes of functions are established. Numerical tests indicate that the method compares favorably with existing methods.

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“…Restricting the domain of the functions to the real axis, the system (45) is a complete orthonormal system for L p (−∞; ∞), 1¡p¡∞ [14], equipped with the inner product …”

Section: Functions Holomorphic In a Half-planementioning

confidence: 99%