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Approximation and Interpolation of Singular Measures by Trigonometric Polynomials
Complex valued measures of finite total variation are a powerful signal model in many applications. Restricting to the d -dimensional torus, finitely...
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Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs
We provide a new approach to the optimization of trigonometric polynomials with crystallographic symmetry. This approach widens the bridge between...
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Factoring non-negative operator valued trigonometric polynomials in two variables
It is shown using Schur complement techniques that on finite dimensional Hilbert spaces, a non-negative operator valued trigonometric polynomial in...
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Approximation of Generalized Poisson Integrals by Interpolating Trigonometric Polynomials
We establish asymptotically unimprovable interpolation analogs of Lebesgue-type inequalities for 2 π -periodic functions f that can be represented in...
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Approximation in Variable Exponent Spaces and Growth of Norms of Trigonometric Polynomials
Using a variant of Nikol’skii–Stechkin inequality we investigate the approximation problems in Holder type spaces connected with variable exponent...
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The minimum modulus of Gaussian trigonometric polynomials
We prove that the minimum of the modulus of a random trigonometric polynomial with Gaussian coefficients, properly normalized, has limiting...
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Symbolic Treatment of Trigonometric Parametrizations: The General Unirational Case and Applications
In this paper, we consider symbolic (hybrid trigonometric) parametrizations defined as tuples of real rational expressions involving circular and...
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Trigonometric series and the permutation sign convergence condition
We prove that a uniformly convergent trigonometric series may not satisfy the permutation sign convergence condition, hence it may not satisfy the...
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An introduction to a hybrid trigonometric box spline surface producing subdivision scheme
Trigonometric box splines can be considered as the multivariate generalizations of univariate B-splines. This means multivariate trigonometric box...
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Positive Polynomials with Zeros
Chapter 6 studies extensions of the strict positivstellensätze from Chapter 5 to non-negative polynomials. The most important tool is the Archimedean...
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Construction of Solutions of the Helmholtz Equation in a Cylindrical Coordinate System in the Form of Homogeneous Polynomials in Two Biorthogonal Systems of Functions
We construct a system of solutions for the coefficients of expansion in the system of trigonometric functions for the solution of the Helmholtz...
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Rational quadratic trigonometric spline fractal interpolation functions with variable scalings
Fractal interpolation function (FIF) constructed through an iterated function system is more versatile than any classical spline interpolation. In...
