On Asymptotically OrthonormalSequences
Canadian journal of mathematics, Tome 69 (2017) no. 6, pp. 1312-1337

Voir la notice de l'article provenant de la source Cambridge University Press

An asymptotically orthonormal sequence is a sequence that is nearly orthonormal in the sense that it satisfies the Parseval equality up to two constants close to one. In this paper, we explore such sequences formed by normalized reproducing kernels for model spaces and de Branges–Rovnyak spaces.
DOI : 10.4153/CJM-2017-001-9
Mots-clés : 30J05, 30H10, 46E22, function space, de Branges-Rovnyak and model space, reproducing kernel, asymptotically orthonormal sequence
Fricain, Emmanuel; Rupam, Rishika. On Asymptotically OrthonormalSequences. Canadian journal of mathematics, Tome 69 (2017) no. 6, pp. 1312-1337. doi: 10.4153/CJM-2017-001-9
@article{10_4153_CJM_2017_001_9,
     author = {Fricain, Emmanuel and Rupam, Rishika},
     title = {On {Asymptotically} {OrthonormalSequences}},
     journal = {Canadian journal of mathematics},
     pages = {1312--1337},
     year = {2017},
     volume = {69},
     number = {6},
     doi = {10.4153/CJM-2017-001-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-001-9/}
}
TY  - JOUR
AU  - Fricain, Emmanuel
AU  - Rupam, Rishika
TI  - On Asymptotically OrthonormalSequences
JO  - Canadian journal of mathematics
PY  - 2017
SP  - 1312
EP  - 1337
VL  - 69
IS  - 6
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-001-9/
DO  - 10.4153/CJM-2017-001-9
ID  - 10_4153_CJM_2017_001_9
ER  - 
%0 Journal Article
%A Fricain, Emmanuel
%A Rupam, Rishika
%T On Asymptotically OrthonormalSequences
%J Canadian journal of mathematics
%D 2017
%P 1312-1337
%V 69
%N 6
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-2017-001-9/
%R 10.4153/CJM-2017-001-9
%F 10_4153_CJM_2017_001_9

[1] [1] Baranov, A. D., Bernstein-type inequalities for shift-coinvariant subspaces and their applications to Carleson embeddings. J. Funct. Anal. 223(2005), no. 1,116–146. http://dx.doi.Org/10.1016/j.jfa.2OO4.08.014 Google Scholar

[2] [2] Baranov, A. D., Stability of bases and frames of reproducing kernels in model spaces. Annales de l'Institut 2399–2422. Google Scholar | DOI

[3] [3] Baranov, A., Fricain, E., and Mashreghi, J., Weighted norm inequalities for de Branges-Rovnyak spaces and their applications. Amer. J. Math. 132(2010), no. 1,125–155. Google Scholar

[4] [4] Chalendar, I., Fricain, E., and Timotin, D., Functional models and asymptotically orthonormal sequences. Annales de l'Institut Fourier 53(2003), no. 5,1527–1549. http://dx.doi.Org/10.58O2/aif.1987 Google Scholar

[5] [5] Cohn, W. S., Carleson measures and operators on sta-invariant subspaces. J. Operator Theory 15(1986), no. 1, 181–202. Google Scholar

[6] [6] de Branges, L. and Rovnyak, J., Canonical models in quantum scattering theory. In: Perturbation theory and its Applications in Quantum Mechanics, 1966, pp. 295–392. Google Scholar

[7] [7] Rovnyak, J.,, Square summable power series. Courier Corporation, 2015. Google Scholar

[8] [8] Fricain, E. and Mashreghi, J., Boundary behavior of functions in the de Branges-Rovnyak spaces. Complex Analysis Operator Theory 2(2008), no. 1, 87–97. Google Scholar | DOI

[9] [9] Fricain, E., The theory ofℋ(b) spaces. Vol. 1, New Mathematical Monographs, 20, Cambridge University Press, Cambridge, 2016. http://dx.doi.Org/10.1017/CBO9781139226752 Google Scholar

[10] [10] Garcia, S. R., Mashreghi, J., and Ross, W. T., Introduction to model spaces and their operators. Cambridge Studies in Advanced Mathematics, 148, Cambridge University Press, Cambridge, 2016. Google Scholar | DOI

[11] [11] Gorkin, P., J. McCarthy, E., Pott, S., and Wick, B. D., Thin sequences and the Gram matrix. Arch. Math. 103(2014), 93–99. http://dx.doi.Org/10.1007/s00013-014-0667-8 Google Scholar

[12] [12] Hruschev, S. V., Nikolskii, N. K., and Pavlov, B.S., Unconditional hases of exponentials and of reproducing kernels. In: Complex analysis and spectral theory (Leningrad, 1979/1980), Lecture Notes in Math., 864, Springer, Berlin-New York, 1981, pp. 214–335. Google Scholar

[13] [13] Levinson, N., Gap and density theorems. American Mathematical Society Colloquium Publications, 26, American Mathematical Society, New York, 1940. Google Scholar

[14] [14] Nikolski, N. K., Treatise on the shift operator-spectral function theory. Grundlehren der Mathematischen Wissenschaften, 273, Springer-Verlag, Berlin-Heidelberg, 1986. Google Scholar | DOI

[15] [15] Nikolski, N. K., Operators, functions, and systems - an easy reading: Hardy, Hankel, and Toeplitz. American Mathematical Society, Providence, RI, 2009. Google Scholar

[16] [16] R. P. and Wiener, N., Fourier transforms in the complex domain. American Mathematical Society Colloquium Publications, 19, American Mathematical Society, Providence, RI, 1987. Google Scholar

[17] [17] Sarason, D., Sub-Hardy Hilbert spaces in the unit disk. University of Arkansas Lecture Notes in the Mathematical Sciences, 10, John Wiley & Sons, Inc., New York, 1994. Google Scholar

[18] [18] Vinogradov, S. A. and Havin, V. P., Free interpolation in H∞ and in certain other classes of functions. I. Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 47(1974), 15-54, 184–185,191. Google Scholar

[19] [19] Volberg, A., Two remarks concerning the theorem ofS. Axler, S.-Y.A. Chang, and D. Sarason. J. Operator Theory 8(1982), 209–218. Google Scholar

[20] [20] Young, R. M., An introduction to nonharmonic Fourier series. First ed., Academic Press, Inc., San Diego, CA, 2001. Google Scholar

Cité par Sources :