Abstract:
The notion of a frame in a Banach space with respect to a model space of sequences is introduced. This notion is different from the notions of an atomic decomposition, Banach frame in the sense of Gröchenig, (unconditional) Schauder frame in the sense of Han and Larson, and other known definitions of frames for Banach spaces. The frames introduced in this paper are shown to play a universal role in the solution of the general problem of representation of functions by series. A projective description of these frames is given. A criterion for the existence of a linear frame expansion algorithm and an analogue of the extremality property for a frame expansion are obtained.
This publication is cited in the following 19 articles:
Ilya Izbiakov, Sergey Novikov, Pavel Terekhin, “Complement property and frames in the phase retrieval problem”, Funct. Anal. Appl., 59:1 (2025), 11–18
P. A. Terekhin, “Ortorekursivnye razlozheniya, porozhdennye yadrom Sege”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 23:4 (2023), 443–455
K. Mahesh Krishna, “FUNCTIONAL DEUTSCH UNCERTAINTY PRINCIPLE”, SSRN Journal, 2023
Anton Baranov, Timur Batenev, “Representing Systems of Reproducing Kernels in Spaces of Analytic Functions”, Results Math, 78:4 (2023)
K. Mahesh Krishna, P. Sam Johnson, “Frames for Metric Spaces”, Results Math, 77:1 (2022)
K. Mahesh Krishna, “Metric, Schauder and Operator-Valued Frames (PhD Thesis)”, SSRN Journal, 2022
K. S. Speransky, “On the convergence of the order-preserving weak greedy algorithm for subspaces generated by the Szegö kernel in the Hardy space”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 21:3 (2021), 336–342
Yu. A. Farkov, “Freimy v analize Uolsha, matritsy Adamara i ravnomerno raspredelennye mnozhestva”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g. Chast 1, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 199, VINITI RAN, M., 2021, 17–30
K. Mahesh Krishna, P. Sam Johnson, “New identity on Parseval p-approximate Schauder frames and applications”, Journal of Interdisciplinary Mathematics, 24:7 (2021), 1751
S. V. Astashkin, P. A. Terekhin, “Representation of functions in symmetric spaces by dilations and translations”, Funct. Anal. Appl., 54:1 (2020), 45–48
Astashkin V S. Terekhin P.A., “Representing Systems of Dilations and Translations in Symmetric Function Spaces”, J. Fourier Anal. Appl., 26:1 (2020)
K. S. Speransky, P. A. Terekhin, “On existence of frames based on the Szegö kernel in the Hardy space”, Russian Math. (Iz. VUZ), 63:2 (2019), 51–61
Poumai Kh.T., Jahan Sh., “Atomic Systems For Operators”, Int. J. Wavelets Multiresolut. Inf. Process., 17:1 (2019), 1850066
Speransky K.S., Terekhin P.A., “A Representing System Generated By the Szego Kernel For the Hardy Space”, Indag. Math.-New Ser., 29:5 (2018), 1318–1325
Jahan Sh., Kumar V., Kaushik S.K., “On the Existence of Non-Linear Frames”, Arch. Math.-Brno, 53:2 (2017), 101–109
Poumai Kh.T., Kaushik S.K., “Some Results Concerning Riesz Bases and Frames in Banach Spaces”, Jordan J. Math. Stat., 10:1 (2017), 11–32
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