The convolution structure for Jacobi function expansions

DOI10.1007/BF02388521zbMath0267.42009OpenAlexW2016224749MaRDI QIDQ2562989

Mogens Flensted-Jensen, Koornwinder, Tom H.

Publication date: 1973

Published in: Arkiv för Matematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02388521

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Harmonic analysis and spherical functions (43A90)

Related Items

Spherical maximal operator on symmetric spaces of constant curvature, Best trigonometric approximation and Dini-Lipschitz classes, Patterns and structure in systems governed by linear second-order differential equations, On support properties of functions and their Jacobi transform, Uncertainty principles for the Heckman-Opdam transform, On the product formula and convolution associated with the index Whittaker transform, A new product formula involving Bessel functions, Some new estimates for the Jacobi transform in the space \(L_{2}(\mathbb{R}^{+}, J^{\alpha,\beta}(x)dx)\), Laws of large numbers for hypergroups on \({\mathbb{R}}_+\), A note on \(K\)-functional, modulus of smoothness, Jackson theorem and Bernstein-Nikolskii-Stechkin inequality on Damek-Ricci spaces, Applications of alpha space, Convolution structure associated with the Jacobi-Dunkl operator on \(\mathbb R\), One-dimensional hypergroups, Fractional Fourier-Jacobi type transform, Mehler integral transform associated with Jacobi functions with respect to the dual variable, Some continuous analogs of the expansion in Jacobi polynomials and vector-valued orthogonal bases, Integrability of conformal blocks. I: Calogero-Sutherland scattering theory, Generalized translation and convolution associated to the linear canonical Fourier–Jacobi transform, On algebras of double cosets of symmetric groups with respect to Young subgroups, Translation beyond Delsarte, Absolutely convergent Fourier–Jacobi series and generalized Lipschitz classes, Weighted integrability of Fourier–Jacobi transforms, Mehler–Fock transforms and retarded radiative Green functions in hyperbolic and spherical spaces, НЕКОТОРЫЕ ЭКСТРЕМАЛЬНЫЕ ЗАДАЧИ ДЛЯ ПРЕОБРАЗОВАНИЯ ФУРЬЕ ПО СОБСТВЕННЫМ ФУНКЦИЯМ ОПЕРАТОРА ШТУРМА–ЛИУВИЛЛЯ, НЕКОТОРЫЕ ЭКСТРЕМАЛЬНЫЕ ЗАДАЧИ ГАРМОНИЧЕСКОГО АНАЛИЗА И ТЕОРИИ ПРИБЛИЖЕНИЙ, Вторая экстремальная задача Логана для преобразования Фурье по собственным функциям оператора Штурма–Лиувилля, Integral representations of pseudo-differential operator associated with the Jacobi differential operator, Generalized Lipschitz conditions for absolute convergence of weighted Jacobi-Dunkl series, Heat ``polynomials for a singular differential operator on (0,\(\infty)\), Crossing symmetry in alpha space, Weighted approximation for the generalized discrete Fourier-Jacobi transform on space \(L_p(\mathbb{T})\), Jacobi Transform of (ν,γ,p)-Jacobi–Lipschitz Functions in the Space Lp(R+,Δ(α,β)(t)dt), Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications, Weighted norm inequalities for integral transforms, Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L₂ metric: Jackson's type direct theorems, Spherical maximal operator on symmetric spaces, an end point estimate, The representation of the trilinear kernel in general orthogonal polynomials and some applications, Product Formulas and Convolutions for Angular and Radial Spheroidal Wave Functions, A product formula and a convolution structure for a \(k\)-Hankel transform on \(\mathbb{R}\), Applications of an inverse Abel transform for Jacobi analysis: weak-\(L^1\) estimates and the Kunze-Stein phenomenon, Lipschitz conditions for the generalized discrete Fourier transform associated with the Jacobi operator on \([0, \pi\)], The Delsarte extremal problem for the Jacobi transform, New inversion formulas for the horospherical transform, An operational sum method with tchebycheff series expansions for solving difference equations, Convolution operators on Schwartz spaces for Chébli--Trimèche hypergroups, New recurrence relations for Wilson polynomials via a system of Jacobi type orthogonal functions, Estimates of functionals by deviations of Steklov type averages generated by Dunkl type operators, On the norms of generalized translation operators generated by Dunkl type operators, Positive convolution structure for a class of Heckman-Opdam hypergeometric functions of type BC, Elliptic transmutation I, On a weak \(L^1\) property of maximal operators on non-compact semisimple Lie groups, Hilbert transform and related topics associated with the differential Jacobi operator on \((0, +\infty)\), On the kernel of the product formula on symmetric spaces, A new proof of a Paley-Wiener type theorem for the Jacobi transform, Unnamed Item, Hypoelliptic Jacobi convolution operators on Schwartz distributions, Bohman extremal problem for the Jacobi transform, Equivalence of K-functionals and modulus of smoothness constructed by generalized Jacobi transform, Group theoretic nature of certain recursion relations for singular Cauchy problems, On the integrability of Fourier-Jacobi transforms, Growth properties of Fourier transforms via moduli of continuity, Characterising extended Lipschitz type conditions with moduli of continuity, Jacobi functions: the addition formula and the positivity of the dual convolution structure, Approximation of the multidimensional Jacobi transform in \(L_2\) by partial integrals, Fourier–Jacobi harmonic analysis and some problems of approximation of functions on the half-axis in L₂ metric: Nikol'skii–Besov type function spaces, Pseudo-differential operators associated with the Jacobi differential operator, Convolution of orbital measures on symmetric spaces: A survey, Atomic decomposition of a real Hardy space for Jacobi analysis, CONVOLUTION OF ORBITAL MEASURES ON SYMMETRIC SPACES OF TYPE AND, Singular integral operators of convolution type on Jacobi hypergroup, Hardy spaces and maximal operators on real rank one semisimple Lie groups. I, Non-integrable multipliers for the Jacobi transform, Pseudo-differential operators associated with the Jacobi differential operator and Fourier-cosine wavelet transform, Conditions for the \(L_{p, \lambda}\)-boundedness of the Riesz potential generated by the Gegenbauer differential operator, Radon, cosine and sine transforms on real hyperbolic space, Quantitative uncertainty principles related to Lions transform, Optimal argument in the sharp Jackson inequality in the space \(L_2\) with hyperbolic weight, Variation diminishing convolution kernels associated with second-order differential operators, Hypergroups associated to harmonic NA groups, Sobolev type spaces associated with jacobi differential operators, Convolution semigroups and central limit theorem associated with a dual convolution structure, Integrability of the Fourier–Jacobi transform of functions satisfying Lipschitz and Dini–Lipschitz-type estimates

Cites Work