[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2021.29.4.725

SHARPENING LOWER BOUND IN SOME INEQUALITIES FOR FRAMES IN HILBERT SPACES

Sultanzadeh, Fahimeh (Department of Mathematics, Mashhad Branch, Islamic Azad University)
Hassani, Mahmood (Department of Mathematics, Mashhad Branch, Islamic Azad University)
Omidvar, Mohsen Erfanian (Department of Mathematics, Mashhad Branch, Islamic Azad University)
Gol, Rajab Ali kamyabi (Department of Pure Mathematics, Ferdowsi University of Mashhad)

Publication Information

Korean Journal of Mathematics / v.29, no.4, 2021 , pp. 725-732 More about this Journal

Abstract

This paper aims to present a new lower bound for some inequalities related to Frames in Hilbert space. Some refinements of the inequalities for general frames and alternate dual frames under suitable conditions are given. These results refine the remarkable results obtained by Balan et al. and Gavruta.

Keywords

Hilbert space; Frame; Parseval frame;

Citations & Related Records

Reference

1	R. Balan, P.G. Casazza, D. Edidin, G. Kutyniok, A new identity for Parseval frames , Proc. Amer. Math. Soc. 135 (2007) 1007-1015. DOI
2	P.G. Casazza, The art of frame theory, Taiwanese J. Math. 4 (2000) 129-201. DOI
3	P.G. Casazza, G. Kutyniok, Frames of subspaces , Wavelets, frames and operator theory, Contemp. Math., 345, Amer. Math. Soc., Providence, RI, 2004. 87-113. DOI
4	O. Christensen, An introduction to frames and Riesz bases, Birkhauser/ springer [cham] (2016).
5	J. Duffin, A.C. Schaeffer, A class of nonharmonic Fiurier series, Trans. Amer. Math. Soc. 72 (1952) 341-366. DOI
6	Q.P. Guo, J.S. Leng, H.B. Li, Some equalities and inequalities for fusion frames , Springer Plus. 5 (2016) , Article ID 121, 10 pages.
7	Y.C. Eldar, G.D. Forney Jr., Optimal tight frames and quantum measurement, IEEE Trans. Inform. Theory 48 (2002) 599-610. DOI
8	P. Gavruta, On some identities and inequalities for frames in Hilbert spaces, J. Math. Anal. Appl. 321 (2006) 469-478. DOI
9	D. Han, D.R. Larson, Frames, bases and group representations, Mem. Amer. Math. Soc. 147 (2000), x+94 pp.
10	R. Vale and S. Waldron, Tight frames and their symmetries , Constr. Approx. 21 (2005) 83-112. DOI
11	L. Zou, Y. Jiang, Improved arithmetic-geometric mean inequality and its application, J. Math. Inequal. 9 (2015) 107-111.
12	L. Gavruta, Frames for operators , Appl Comput Harmon Anal, 32 (2012) 139-144. DOI
13	I. Daubechies, Ten Lectures on Wavelets, SIAM, Philadelphia, PA (1992).