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Weighted integral Hankel operators with continuous spectrum

100%
Fedele E., Pushnitski A.
Concrete Operators
|
2017
|
tom 4
|
nr 1
121-129
EN
Using the Kato-Rosenblum theorem, we describe the absolutely continuous spectrum of a class of weighted integral Hankel operators in L2(ℝ+). These self-adjoint operators generalise the explicitly diagonalisable operator with the integral kernel sαtα(s + t)-1-2α, where α > -1/2. Our analysis can be considered as an extension of J. Howland’s 1992 paper which dealt with the unweighted case, corresponding to α = 0.
2
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Multipliers and Wiener-Hopf operators on weighted L p spaces

81%
Petkova V.
Open Mathematics
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2013
|
tom 11
|
nr 3
561-573
EN
We study multipliers M (bounded operators commuting with translations) on weighted spaces L ω p (ℝ), and establish the existence of a symbol µM for M, and some spectral results for translations S t and multipliers. We also study operators T on the weighted space L ω p (ℝ+) commuting either with the right translations S t , t ∈ ℝ+, or left translations P +S −t , t ∈ ℝ+, and establish the existence of a symbol µ of T. We characterize completely the spectrum σ(S t ) of the operator S t proving that $\sigma (S_t ) = \{ z \in \mathbb{C}:|z| \leqslant e^{t\alpha _0 } \} ,$ where α 0 is the growth bound of (S t )t≥0. A similar result is obtained for the spectrum of (P +S −t ), t ≥ 0. Moreover, for an operator T commuting with S t , t ≥ 0, we establish the inclusion [...] , where \(\mathcal{O}\) = {z ∈ ℂ: Im z α 0}.
3
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Properties of two variables Toeplitz type operators

81%
Król-Klimkowska E., Ptak M.
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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2016
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tom 15
EN
The investigation of properties of generalized Toeplitz operators with respect to the pairs of doubly commuting contractions (the abstract analogue of classical two variable Toeplitz operators) is proceeded. We especially concentrate on the condition of existence such a non-zero operator. There are also presented conditions of analyticity of such an operator.
4
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Reducing subspaces for multiplication operators on the Dirichlet space through local inverses and Riemann surfaces

81%
Gu C., Luo S., Xiao J.
Complex Manifolds
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2017
|
tom 4
|
nr 1
84-119
EN
This paper gives a full characterization of the reducing subspaces for the multiplication operator Mϕ on the Dirichlet space with symbol of finite Blaschke product ϕ of order 5I 6I 7. The reducing subspaces of Mϕ on the Dirichlet space and Bergman space are related. Our strategy is to use local inverses and Riemann surfaces to study the reducing subspaces of Mϕ on the Bergman space. By this means, we determine the reducing subspaces of Mϕ on the Dirichlet space and answer some questions of Douglas-Putinar-Wang in [6].
5
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Toeplitz operators and Wiener-Hopf factorisation: an introduction

62%
Câmara M. C.
Concrete Operators
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2017
|
tom 4
|
nr 1
130-145
EN
Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces Hp of the upper half-plane and we review how their Fredholm properties can be studied in terms of a Wiener-Hopf factorisation of their symbols, obtaining necessary and sufficient conditions for the operator to be Fredholm or invertible, as well as formulae for their inverses or one-sided inverses when these exist. The results are applied to a class of singular integral equations in L−1(ℝ)
6
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A Riemann-Hilbert problem with a vanishing coefficient and applications to Toeplitz operators

52%
Perälä A., Virtanen J. A., Wolf L.
Concrete Operators
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2013
|
tom 1
28-36
EN
We study the homogeneous Riemann-Hilbert problem with a vanishing scalar-valued continuous coefficient. We characterize non-existence of nontrivial solutions in the case where the coefficient has its values along several rays starting from the origin. As a consequence, some results on injectivity and existence of eigenvalues of Toeplitz operators in Hardy spaces are obtained.
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