FRAMES AND REPRESENTING SYSTEMS IN FRECHET SPACES AND THEIR DUALS

被引：3

作者：

Bonet, J. ^{[1
]}

Fernandez, C. ^{[2
]}

Galbis, A. ^{[2
]}

Ribera, J. M. ^{[1
]}

机构：

[1] Univ Politecn Valencia, IUMPA, E-46071 Valencia, Spain

[2] Univ Valencia, Dept Anal Matemat, E-46100 Valencia, Spain

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2017年 / 11卷 / 01期

关键词：

frames; representing systems; Frechet spaces; (LB)-spaces; weakly sufficient sets; SUFFICIENT SETS; EXPANSIONS;

D O I：

10.1215/17358787-3721183

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Frames and Bessel sequences in Fr\'echet spaces and their duals are defined and studied. Their relation with Schauder frames and representing systems is analyzed. The abstract results presented here, when applied to concrete spaces of analytic functions, give many examples and consequences about sampling sets and Dirichlet series expansions.

引用

页码：1 / 20

页数：20

共 29 条

[1] DUAL OF THE FUNCTION ALGEBRA A-∞(D) AND REPRESENTATION OF FUNCTIONS IN DIRICHLET SERIES [J].

Abanin, A. V. ;

Khoi, Le Hai .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (10) :3623-3635

[2]

Abanin A. V., 2013, SIBERIAN MATH J, V54, P575, DOI DOI 10.1134/S0037446613040010

[3] CERTAIN CRITERIA FOR WEAK SUFFICIENCY [J].

ABANIN, AV .

MATHEMATICAL NOTES, 1986, 40 (3-4) :757-764

[4]

Abanina T. I., 2013, NAUCHNOE OBOZRENIE, V9, P101

[5]

Berenstein CA., 1995, Complex Analysis and Special Topics in Harmonic Analysis, DOI [10.1007/978-1-4613-8445-8, DOI 10.1007/978-1-4613-8445-8]

[6] A PROJECTIVE DESCRIPTION OF WEIGHTED INDUCTIVE LIMITS [J].

BIERSTEDT, KD ;

MEISE, R ;

SUMMERS, WH .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 272 (01) :107-160

[7] Sampling sets and sufficient sets for A-∞ [J].

Bonet, J ;

Domanski, P .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2003, 277 (02) :651-669

[8] Shrinking and boundedly complete Schauder frames in Frechet spaces [J].

Bonet, Jose ;

Fernandez, Carmen ;

Galbis, Antonio ;

Ribera, Juan M. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2014, 410 (02) :953-966

[9] The reconstruction formula for Banach frames and duality [J].

Carando, Daniel ;

Lassalle, Silvia ;

Schmidberg, Pablo .

JOURNAL OF APPROXIMATION THEORY, 2011, 163 (05) :640-651

[10] Frame expansions in separable Banach spaces [J].

Casazza, P ;

Christensen, O ;

Stoeva, DT .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 307 (02) :710-723

← 1 2 3 →