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Data approximation in twisted shift-invariant spaces
Twisted convolution is a non-standard convolution which arises while transferring the convolution of the Heisenberg group to the complex plane. Under...
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Representations and Regularity of Vector-Valued Right-Shift Invariant Operators Between Half-Line Bessel Potential Spaces
Representation and boundedness properties of linear, right-shift invariant operators on half-line Bessel potential spaces (also known as...
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Cyclic Vectors and Invariant Subspaces of the Backward Shift Operator in Schwartz Modules
AbstractCyclic vectors and proper closed invariant subspaces of the backward shift operator in the Schwartz modules of entire functions of...
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Average sampling expansions from regular and irregular samples over shift-invariant subspaces on LCA groups
Let G be a second countable locally compact abelian group and H a countable closed discrete subgroup of G such that the quotient group G / H is...
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Approximation of kernel projection operators in shift-invariant subspaces of function spaces with mixed norms
In this paper, we study the approximation problems of the kernel projection operators with mixed norms. Moreover, we give the approximation order for...
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Symmetric shift-invariant subspaces and harmonic maps
The Grassmannian model represents harmonic maps from Riemann surfaces by families of shift-invariant subspaces of a Hilbert space. We impose a...
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Harmonic maps and shift-invariant subspaces
With the help of operator-theoretic methods, we derive new and powerful criteria for finiteness of the uniton number for a harmonic map from a...
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Analytic Functions in Local Shift-Invariant Spaces and Analytic Limits of Level Dependent Subdivision
In this paper we characterize all subspaces of analytic functions in finitely generated shift-invariant spaces with compactly supported generators...
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The functional equations of Langlands Eisenstein series for SL(n, ℤ)
In this paper, we present a very simple explicit description of Langlands Eisenstein series for SL( n , ℤ). The functional equations of these...
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Right-Sided Invertibility of Binomial Functional Operators and Graded Dichotomy
In this paper, we consider the right-sided invertibility problem for binomial functional operators. It is known that such operators are invertible...
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Phillips symmetric operators and functional calculus of maximal symmetric operators
The aim of this work is to develop a functional calculus for simple maximal symmetric operators. The proposed approach is based on the properties of...
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Complements in Functional Analysis
Functional analysis deals with properties of spaces of functions (or of sequences), rather than of individual objects. To study a specific function...
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The Functional Central Limit Theorem for Ergodic Markov Processes
In this chapter a broadly applicable functional central limit theorem for continuous parameter ergodic Markov processes is developed. This uses the...
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Dilation Theory and Functional Models for Tetrablock Contractions
A classical result of Sz.-Nagy asserts that a Hilbert space contraction operator T can be dilated to a unitary...
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Functional Models of Symmetric and Selfadjoint Operators
Let A be a closed simple symmetric operator with equal defect numbers acting in a Hilbert space, and let...