Quadrature formulas for rational functions.
Quantized orthonormal systems: A non-commutative Kwapień theorem
The concepts of Riesz type and cotype of a given Banach space are extended to a non-commutative setting. First, the Banach space is replaced by an operator space. The notion of quantized orthonormal system, which plays the role of an orthonormal system in the classical setting, is then defined. The Fourier type and cotype of an operator space with respect to a non-commutative compact group fit in this context. Also, the quantized analogs of Rademacher and Gaussian systems are treated. All this is...
Quasi-definiteness of generalized Uvarov transforms of moment functionals.
Quasi-orthogonality on the unit circle and semi-classical forms.
Radial Subspaces of Besov and Lizorkin-Triebel Classes: Extended Strauss Lemma and Compactness of Embeddings.
Random perturbations of exponential Riesz bases in
Let a sequence be given such that the exponential system forms a Riesz basis in and be a sequence of independent real-valued random variables. We study the properties of the system as well as related problems on estimation of entire functions with random zeroes and also problems on reconstruction of bandlimited signals with bandwidth via their samples at the random points .
Rates of Convergence for the Approximation of Dual Shift-Invariant Systems in ... (...).
Rearrangements of periodic multiplicative orthogonal series
Recent developments in the theory of function spaces with dominating mixed smoothness
The aim of these lectures is to present a survey of some results on spaces of functions with dominating mixed smoothness. These results concern joint work with Winfried Sickel and Miroslav Krbec as well as the work which has been done by Jan Vybíral within his thesis. The first goal is to discuss the Fourier-analytical approach, equivalent characterizations with the help of derivatives and differences, local means, atomic and wavelet decompositions. Secondly, on this basis we study approximation...
Recent developments in the theory of Haar series
Recent developments in the theory of Walsh series.
Recent trends on analytic properties of matrix orthonormal polynomials.
Reconstruction in time-warped weighted shift-invariant spaces with application to spline subspaces.
Recovery of band-limited functions on locally compact Abelian groups from irregular samples
Using the techniques of approximation and factorization of convolution operators we study the problem of irregular sampling of band-limited functions on a locally compact Abelian group . The results of this paper relate to earlier work by Feichtinger and Gröchenig in a similar way as Kluvánek’s work published in 1969 relates to the classical Shannon Sampling Theorem. Generally speaking we claim that reconstruction is possible as long as there is sufficient high sampling density. Moreover, the iterative...
Recurrence relations for orthogonal polynomials on algebraic curves
Recurrence relations for the coefficients of expansions in classical orthogonal polynomials of a discrete variable
A method is given to find a recurrence relation for the coefficients of the series expansion of a function f with respect to classical orthogonal polynomials of a discrete variable, which follows from a linear difference equation satisfied by f.
Recurrence relations with periodic coefficients and Chebyshev polynomials
We show that polynomials defined by recurrence relations with periodic coefficients may be represented with the help of Chebyshev polynomials of the second kind.
Recurrences for the coefficients of series expansions with respect to classical orthogonal polynomials
Let be any sequence of classical orthogonal polynomials. Further, let f be a function satisfying a linear differential equation with polynomial coefficients. We give an algorithm to construct, in a compact form, a recurrence relation satisfied by the coefficients in . A systematic use of the basic properties (including some nonstandard ones) of the polynomials results in obtaining a low order of the recurrence.
Refinement equations for generalized translations.
Refinement Equations with Nonnegative Coefficients.