Displaying similar documents to “On the spectrum of the distributional kernel related to the residue.”

A la recherche du spectre perdu: An invitation to nonlinear spectral theory

Appell, Jürgen

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We give a survey on spectra for various classes of nonlinear operators, with a particular emphasis on a comparison of their advantages and drawbacks. Here the most useful spectra are the asymptotic spectrum by M. Furi, M. Martelli and A. Vignoli (1978), the global spectrum by W. Feng (1997), and the local spectrum (called “phantom”) by P. Santucci and M. Väth (2000). In the last part we discuss these spectra for homogeneous operators (of any degree), and derive a discreteness result...

On the relationships between Fourier-Stieltjes coefficients and spectra of measures

Przemysław Ohrysko, Michał Wojciechowski (2014)

Studia Mathematica

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We construct examples of uncountable compact subsets of complex numbers with the property that any Borel measure on the circle group with Fourier coefficients taking values in this set has a natural spectrum. For measures with Fourier coefficients tending to 0 we construct an open set with this property. We also give an example of a singular measure whose spectrum is contained in our set.

Fourier-Feynman transforms of unbounded functionals on abstract Wiener space

Byoung Kim, Il Yoo, Dong Cho (2010)

Open Mathematics

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Huffman, Park and Skoug established several results involving Fourier-Feynman transform and convolution for functionals in a Banach algebra S on the classical Wiener space. Chang, Kim and Yoo extended these results to abstract Wiener space for a more generalized Fresnel class ℱ 𝒜 1 , 𝒜 2 A1,A2 than the Fresnel class ℱ (B)which corresponds to the Banach algebra S. In this paper we study Fourier-Feynman transform, convolution and first variation of unbounded functionals on abstract Wiener space...

On discrete Fourier spectrum of a harmonic with random frequency modulation

Waldemar Popiński (2013)

Applicationes Mathematicae

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Asymptotic properties of the Discrete Fourier Transform spectrum of a complex monochromatic oscillation with frequency randomly distorted at the observation times t=0,1,..., n-1 by a series of independent and identically distributed fluctuations is investigated. It is proved that the second moments of the spectrum at the discrete Fourier frequencies converge uniformly to zero as n → ∞ for certain frequency fluctuation distributions. The observed effect occurs even for frequency fluctuations...