Geodesic
Bohman extremal problem for the Jacobi transform
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 126-135 Cet article a éte moissonné depuis la source Math-Net.Ru

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We give a solution to the Bohman extremal problem for nonnegative even entire functions of exponential type that are Jacobi transforms of compactly supported functions. We prove that the extremal function is unique. The Gauss quadrature formula on the half-line over zeros of the Jacobi function is used.
Keywords: hyperbolic weight, Jacobi function, Bohman extremal problem
Mots-clés : Jacobi transform, Gauss quadrature formulae. 
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D. V. Gorbachev; V. I. Ivanov. Bohman extremal problem for the Jacobi transform. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 4, pp. 126-135. http://geodesic.mathdoc.fr/item/TIMM_2016_22_4_a12/

[1] Gorbachev D.V., “Ekstremalnaya zadacha Bomana dlya preobrazovaniya Fure–Gankelya”, Izv. TulGU. Estestv. nauki, 2014, no. 4, 5–10

[2] Gorbachev D.V., “Multidimensional extremal Logan's and Bohman's problems”, Methods of Fourier analysis and approximation, Applied and Numerical Harmonic Analysis, eds. M. Ruzhansky and S. Tikhonov, Springer Internat. Publ., Basel, 2016, 43–58 | DOI | MR | Zbl

[3] Gorbachev D., Ivanov V., “Extremal Bohman's problem for Dunkl transform”, 5th Workshop on Fourier Analysis and Related Fields, Book of Abstracts, MTA Renyi Institute, Budapest, 2015, 6

[4] Bohman H., “Approximate Fourier analysis of distribution functions”, Ark. Mat., 4:2 (1961), 99–157 | DOI | MR | Zbl

[5] Bohman W., Gneiting T., Richards D., “Convolution roots of radial positive definite functions with compact support”, Trans. Amer. Math. Soc., 356 (2004), 4655–4685 | DOI | MR

[6] Jeu M. de, “Paley–Wiener theorems for the Dunkl transform”, Trans. Amer. Math. Soc., 358:10 (2006), 4225–4250 | DOI | MR | Zbl

[7] Koornwinder T.H., “Jacobi functions and analysis on noncompact semisimple Lie groups”, Special functions: Group theoretical aspects and applications, eds. R.A. Askey, T.H. Koornwinder and W. Schempp, Reidel, Dordrecht, 1984, 1–85 | DOI | MR | Zbl

[8] Levitan B.M., Sargsyan I.S., Operatory Shturma–Liuvillya i Diraka, Nauka, M., 1988, 432 pp. | MR

[9] Koornwinder T.H., “A new proof of a Paley–Wiener type theorem for the Jacobi transform”, Ark. Mat., 13:1 (1979), 145–159 | MR

[10] Gorbachev D.V., Ivanov V.I., “Kvadraturnye formuly Gaussa i Markova po nulyam sobstvennykh funktsii zadachi Shturma–Liuvillya, tochnye dlya tselykh funktsii eksponentsialnogo tipa”, Mat. sb., 206:8 (2015), 63–98 | DOI | MR | Zbl

[11] Flensted-Jensen M., Koornwinder T.H., “The convolution structure for Jacobi function expansions”, Ark. Mat., 11:1 (1973), 245–262 | DOI | MR | Zbl

[12] Gorbachev D.V., Ivanov V.I., Veprintsev R.A., “Optimal argument in sharp Jackson's inequality in the space $L_2$ with the hyperbolic weight”, Math. Notes, 96:5 (2014), 904–913 | DOI | MR | Zbl

[13] Levin B.Ya., Raspredelenie kornei tselykh funktsii, Gostekhizdat, M., 1956, 632 pp.