Displaying similar documents to “D'Alembert's functional equation on compact groups.”

On the spectral properties of translation operators in one-dimensional tubes

Wojciech Hyb (1991)

Annales Polonici Mathematici

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We study the spectral properties of some group of unitary operators in the Hilbert space of square Lebesgue integrable holomorphic functions on a one-dimensional tube (see formula (1)). Applying the Genchev transform ([2], [5]) we prove that this group has continuous simple spectrum (Theorem 4) and that the projection-valued measure for this group has a very explicit form (Theorem 5).

An approach to joint spectra

Angel Martínez Meléndez, Antoni Wawrzyńczyk (1999)

Annales Polonici Mathematici

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For a given unital Banach algebra A we describe joint spectra which satisfy the one-way spectral mapping property. Each spectrum of this class is uniquely determined by a family of linear subspaces of A called spectral subspaces. We introduce a topology in the space of all spectral subspaces of A and utilize it to the study of the properties of the spectra.

On the differences of the consecutive powers of Banach algebra elements

Helmuth Rönnefarth (1997)

Banach Center Publications

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Let A denote a complex unital Banach algebra. We characterize properties such as boundedness, relative compactness, and convergence of the sequence x n ( x - 1 ) n ∈ ℕ for an arbitrary x ∈ A, using σ(x) and resolvent conditions. Under these circumstances, we investigate elements in the peripheral spectrum, and give further conclusions, also involving the behaviour of x n n ∈ ℕ and 1 / n ∑ k = 0 n - 1 x k n ∈ ℕ .

Bernstein-Sato Polynomials and Spectral Numbers

Andréa G. Guimarães, Abramo Hefez (2007)

Annales de l’institut Fourier

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In this paper we will describe a set of roots of the Bernstein-Sato polynomial associated to a germ of complex analytic function in several variables, with an isolated critical point at the origin, that may be obtained by only knowing the spectral numbers of the germ. This will also give us a set of common roots of the Bernstein-Sato polynomials associated to the members of a μ -constant family of germs of functions. An example will show that this set may sometimes consist of all common...

The truncated matrix trigonometric moment problem with an open gap

Sergey Zagorodnyuk (2015)

Concrete Operators

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This paper is a continuation of our previous investigations on the truncated matrix trigonometric moment problem in Ukrainian Math. J., 2011, 63, no. 6, 786-797, and Ukrainian Math. J., 2013, 64, no. 8, 1199- 1214. In this paper we shall study the truncated matrix trigonometric moment problem with an additional constraint posed on the matrix measure MT(δ), δ ∈ B(T), generated by the seeked function M(x): MT(∆) = 0, where ∆ is a given open subset of T (called a gap). We present necessary...