zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
g-Besselian frames in Hilbert spaces. (English) Zbl 1209.42028
Summary: We introduce the concept of a g-Besselian frame in a Hilbert space and discuss the relations between a g-Besselian frame and a Besselian frame. We also give some characterizations of g-Besselian frames. In the end of this paper, we discuss the stability of g-Besselian frames. Our results show that the relations and the characterizations between a g-Besselian frame and a Besselian frame are different from the corresponding results of g-frames and frames.
MSC:
42C99Non-trigonometric Fourier analysis
42C25Uniqueness and localization for orthogonal series
References:
[1]Duffin, R. J., Schaeffer, A. C.: A class of nonharmonic Fourier series. Trans. Amer. Math. Soc., 72, 341–366 (1952) · doi:10.1090/S0002-9947-1952-0047179-6
[2]Casazza, P. G.: The art of frame theory. Taiwanese J. Math., 4(2), 129–201 (2000)
[3]Christensen, O.: An Introduction to Frames and Riesz Bases, Birkhäuser, Boston, 2003
[4]Fornasier, M.: Quasi-orthogonal decompositions of structured frames. J. Math. Anal. Appl., 289, 180–199 (2004) · Zbl 1058.46009 · doi:10.1016/j.jmaa.2003.09.041
[5]Li, S., Ogawa, H.: Pseudo frames for subspaces with application. J. Fourier Anal. Appl., 10, 409–431 (2004) · Zbl 1058.42024 · doi:10.1007/s00041-004-3039-0
[6]Asgary, M. S., Kosravi, A.: Frames and bases of subspaces in Hilbert spaces. J. Math. Anal. Appl., 308, 541–553 (2005) · Zbl 1091.46006 · doi:10.1016/j.jmaa.2004.11.036
[7]Casazza, P. G., Kutyniok, G.: Frames of Subspaces. Wavelets, Frames and Operator Theory. In: Contemp. Math., Amer. Math. Soc., 345, 2004, 87–113
[8]Casazza, P. G., Kutyniok, G., Li, S.: Fusion frames and distributed processing. Appl. Comput. Harmon. Anal., 25, 114–132 (2008) · Zbl 1258.42029 · doi:10.1016/j.acha.2007.10.001
[9]Găvruta, P.: On the duality of fusion frames. J. Math. Anal. Appl., 333, 871–879 (2007) · Zbl 1127.46016 · doi:10.1016/j.jmaa.2006.11.052
[10]Khosravi, A., Musazadeh, K.: Fusion frames and g-frames. J. Math. Anal. Appl., 342, 1068–1083 (2008)
[11]Ruiz, M. A., Stojanoff, D.: Some properties of frames of subspaces obtained by operator theory methods. J. Math. Anal. Appl., 343, 366–378 (2008)
[12]Christensen, O., Eldar, Y. C.: Oblique dual frames and shift-invariant spaces. Appl. Comput. Harmon. Anal., 17, 48–68 (2004) · Zbl 1043.42027 · doi:10.1016/j.acha.2003.12.003
[13]Sun, W.: G-frames and g-Riesz bases. J. Math. Anal. Appl., 322(1), 437–452 (2006) · Zbl 1129.42017 · doi:10.1016/j.jmaa.2005.09.039
[14]Sun, W.: Stability of g-frames. J. Math. Anal. Appl., 326(2), 858–868 (2006) · Zbl 1130.42307 · doi:10.1016/j.jmaa.2006.03.043
[15]Ding, M. L., Zhu, Y. C.: Stability of g-frames. J. Fuzhou Univ. Nat. Sci. Ed, 35(3), 321–325 (2007)
[16]Zhu, Y. C.: Characterization of g-frames and g-Riesz bases in Hilbert spaces. Acta Mathematica Sinica, English Series, 24(10), 1727–1736 (2008) · Zbl 1247.42031 · doi:10.1007/s10114-008-6627-0
[17]Xiao X. C., Zhu Y. C., Zeng X. M.: Some properties of g-Parseval frames in Hilbert spaces. Acta Mathematica Sinica, Chinese Series, 51(6), 1143–1150 (2008)
[18]Wang Y. J., Zhu Y. C.: G-frames and g-frame sequences in Hilbert spaces. Acta Mathematica Sinica, English Series, 25(12), 2093–2106 (2009) · Zbl 1198.42032 · doi:10.1007/s10114-009-7615-8
[19]Holub, J. R.: Pre-frame operators, Besselian frame, and near-Riesz bases in Hilbert spaces. Proc. Amer. Math. Soc., 122, 79–785 (1994) · doi:10.1090/S0002-9939-1994-1204376-4
[20]Zhu, Y. C.: q-Besselian frames in Banach spaces. Acta Mathematica Sinica, English Series, 23(9), 1707–1718 (2007) · Zbl 1123.42008 · doi:10.1007/s10114-005-0884-y
[21]Christensen, O.: Frame containing a Riesz basis and approximation of the frame coefficients using finitedimensional methods. J. Math. Anal. Appl., 199, 256–270 (1996) · Zbl 0889.46011 · doi:10.1006/jmaa.1996.0140
[22]Casazza, P. G., Christensen, O.: Frames containing a Riesz basis and preservation of this property under perturbations. SIAM J. Math. Anal., 29(1), 266–278 (1998) · Zbl 0922.42024 · doi:10.1137/S0036141095294250