Recombination of stable sampling sets and stable interpolation sets in functional quasinormed spaces
Resumo
This contribution is aimed in obtaining new results in combining stable sampling sets (respectively, stable interpolation sets) of a given quasinormed space in order to obtain other new ones. We apply these results to Paley-Wiener spaces and. In addition, we study the problem of obtaining a generator system of a given quasinormed space, and obtain conditions for a finite product of subsets of a given quasinormed space to be a generator system, using the interpolation and sampling theory for quasinormed spaces of functions.
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Referências
Avantaggiati, A., Loreti, P., Velluci, P., An Explicit Bound for Stability of Sinc Bases, Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics 1 (2015), 473–480, https://doi.org/10.5220/0005512704730480.
Avantaggiati, A., Loreti, P., Velluci, P., Kadec-1/4 Theorem for Sinc Bases, (2016) ArXiv 1603.08762v1.
Avdonin, S. A., On the question of Riesz bases of exponential functions in L2, Vestnik Leningrad Univ. 13 (1974), 5–12 (Russian). English translation in Vestnik Leningrad Univ. Math. 7 (1979), 203–211.
Boas, R.P. Entire Functions, Ed. Academic Press, New York, 1954.
De Carli, L., Concerning Exponential Bases on Multi-Rectangles of Rd, Birkhäuser, Cham., Topics in Classical and Modern Analysis, Applied and Numerical Harmonic Analysis (2019), https://doi.org/10.1007/978-3-030-12277-54.
De Carli, L., Kumar, A., Exponential bases on two dimensional trapezoids, Proc. Amer. Math. Soc. 143 (7) (2015), 2893–2903.
De Carli, L., Mizrahi, A., Tepper, A., Three problems on exponential bases, Canadian Mathematical Bulletin (2019), https://doi.org/10.4153/CMB-2018-015-6.
Kadec, M. I., The exact value of the Paley-Wiener constant, Sov. Math. Dokl. 5 (1964), 559–561.
Kozma, G., Lev, N., Exponential Riesz Bases, Discrepancy of Irrational and BMO, Journal of Fourier Analysis and Applications 17 (2011), 879–898, https://doi.org/10.1007/s00041-011-9178-1.
Kozma, G., Nitzan, S., Combining Riesz bases, Inventiones mathematicae 199 (1) (2015), 267–285, https://doi.org/10.1007/s00222-014-0522-3.
Kozma, G., Nitzan, S., Combining Riesz bases in Rd, Rev. Mat. Iberoam. 32 (4) (2016), 1393–1406, https://doi.org/10.4171/RMI/922.
Levinson, N., Gap and Density Theorems, Colloquium Publications 26, First Edition, American Mathematical Soc., 1940.
Lyubarskii, Y., Seip, K., Sampling and interpolating sequences for multiband-limited functions and exponential bases on disconnected sets, J. Fourier Anal. Appl. 3 (5) (1997), 598–615.
Marzo, J., Riesz basis of exponentials for a union of cubes in Rd, ArXiv:math/0601288, (2006).
Meyer, Y., Nombres de Pisot, nombres de Salem et analyse harmonique, Springer Verlag, Berlin-New York, Lecture Notes in Mathematics 117, 1970.
Meyer, Y., Algebraic numbers and harmonic analysis, North-Holland, Amsterdan, First Edition, 1972.
Olevskii, A.,Ulanovskii, A., On multi-dimensional sampling and interpolation, Anal. Math. Phys. 2 (2) (2012), 149–170.
Olevskii, A., Ulanovskii, A., Functions with Disconnected Spectrum, University Lecture Series, First Edition, American Mathematical Society, 2016.
Paley, R., Wiener, N. Fourier transforms in the complex domain, Amer. Math. Soc. Colloquium Publications 19 (1934).
Sedleckii, A. M., Nonharmonic Fourier Series, Sib. Math. J. 12 (1971a), 793–802.
Sedletskii, A. M., Nonharmonic Analysis, J. Math. Sc. 116 (5) (2009), 3551–3619.
Ullrich, D., Divided differences and systems of nonharmonic Fourier series, Proc. Amer. Math. Soc. 80 (1980), 47–57.
Young, R. M., An introduction to Nonharmonic Fourier Series, Academic Press, Second Edition, 2001.
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