Про характеризацiю фреймiв для операторiв у кватернiонному гiльбертовому просторi

Автор(и)

  • Salma Charfi National School of Electronics and Telecommunications of Sfax, BP 1163, CP 3018 Sfax, Tunisia
  • Hanen Ellouz Faculty of Sciences of Sfax, Department of Mathematics, BP 1171, Sfax 3000 Tunisia

DOI:

https://doi.org/10.15407/mag18.02.194

Ключові слова:

фрейми, атомарнi системи, K-фрейми, кватернiонний гiльбертiв простiр

Анотація

У цiй роботi ми вводимо поняття атомарних систем для операторiв i K-фреймiв у сепарабельних кватернiонних гiльбертових просторах. Цi поняття призводять до узагальнення фреймiв, якi було нещодавно вивчено в [18], i дозволяють нам реконструювати елементи з образа лiнiйного i обмеженого оператора в кватернiонному гiльбертовому просторi.

Mathematical Subject Classification 2010: 42C15, 41A58

Посилання

S.L. Adler, Quaternionic Quantum Mechanics and Quantum Fields, Oxford University Press, New York, 1995.

S. Charfi, A. Jeribi, and I. Walha, Riesz basis property of families of nonharmonic exponentials and application to a problem of a radiation of a vibrating structure in a light fluid, Numer. Funct. Anal. Optim. 32 (2011), 370-382. https://doi.org/10.1080/01630563.2011.555832

S. Charfi, A. Damergi, and A. Jeribi, On a Riesz basis of finite-dimensional invariant subspaces and application to Gribov operator in Bargmann space, Linear Multilinear Algebra 61 (2013), 1577-1591. https://doi.org/10.1080/03081087.2012.753596

S. Charfi and H. Ellouz, Riesz basis of eigenvectors for analytic families of operators and application to a non-symmetrical Gribov operator, Mediterr. J. Math. 15 (2018), No. 6, Paper No. 223. https://doi.org/10.1007/s00009-018-1265-y

S. Charfi and H. Ellouz, Frame of exponentials related to analytic families operators and application to a non-self adjoint problem of radiation of a vibrating structure in a light fluid, Complex Anal. Oper. Theory 13 (2019), No. 3, 839-858. https://doi.org/10.1007/s11785-018-0807-4

O. Christensen, Frames and the projection method, Appl. Comput. Harmon. Anal. 1 (1993), 50-53. https://doi.org/10.1006/acha.1993.1004

O. Christensen, Frame perturbations, Proc. Amer. Math. Soc. 123 (1995), 1217-1220. https://doi.org/10.1090/S0002-9939-1995-1231031-8

O. Christensen, Frames containing a Riesz basis and approximation of the frame coefficients using finite-dimensional methods, J. Math. Anal. Appl. 199 (1996), 256-270. https://doi.org/10.1006/jmaa.1996.0140

O. Christensen, Frames, Riesz bases, and discrete Gabor / wavelet expansions, Bull. Amer. Math. Soc. (N. S.) 38 (2001), 273-291. https://doi.org/10.1090/S0273-0979-01-00903-X

I. Daubechies, A. Grossmann, and Y. Meyer, Painless nonorthogonal expansions, J. Math. Phys. 24 (1986), 1271-1283. https://doi.org/10.1063/1.527388

R.G. Douglas, On majorization, factorization and range inclusion of operators on Hilbert space, Proc. Amer. Math. Soc. 17 (1966), 413-415. https://doi.org/10.1090/S0002-9939-1966-0203464-1

R. J. Duffin and A. C. Schaeffer, A class of nonharmonic Fourier series, Trans. Amer. Math. Soc. 72 (1952), 341-366. https://doi.org/10.1090/S0002-9947-1952-0047179-6

H. Ellouz, I. Feki and A. Jeribi, On a Riesz basis of exponentials related to the eigenvalues of an analytic operator and application to a non-selfadjoint problem deduced from a perturbation method for sound radiation, J. Math. Phys. 54 (2013), 112101. https://doi.org/10.1063/1.4826354

H. Ellouz, I. Feki, and A. Jeribi, On a Riesz basis of exponentials related to a family of analytic operators and application, J. Pseudo-Differ. Oper. Appl. 10 (2019), No.4, 999-1014. https://doi.org/10.1007/s11868-018-0262-z

L. Găvruta, Frames for operators, Appl. Comput. Harmon. Anal. 32 (2012), 139-144. https://doi.org/10.1016/j.acha.2011.07.006

R. Ghiloni, V. Moretti and A. Perotti, Continuous slice functional calculus in quaternionic Hilbert spaces, Rev. Math. Phys. 25 (2013), 11350006. https://doi.org/10.1142/S0129055X13500062

A. Jeribi, Denseness, bases and frames in Banach spaces and applications, De Gruyter, Berlin, 2018. https://doi.org/10.1515/9783110493863

S.K. Sharma and S. Goel, Frames in quaternionic Hilbert spaces, J. Math. Phys. Anal. Geom. 15 (2019), No. 3, 395-411. https://doi.org/10.15407/mag15.03.395

R. M. Young, An introduction to nonharmonic Fourier series, Academic press, London, 1980.

Downloads

Опубліковано

2022-08-20

Як цитувати

(1)
Charfi, S. .; Ellouz, H. . Про характеризацiю фреймiв для операторiв у кватернiонному гiльбертовому просторi. J. Math. Phys. Anal. Geom. 2022, 18, 194-208.

Номер

Розділ

Статті

Завантаження

Дані завантаження ще не доступні.