Analysis of conditions for frame functions, examples with the orthogonal functions

Pilipović, Stevan; Stoeva, Diana T.

doi:10.1080/10652469.2010.541046

Cited by 3 publications

(1 citation statement)

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“…For the present paper we have chosen to stick to the localization concept from [21], because the results obtained for a family of Banach spaces there can naturally be related to Fréchet frames (cf. [28,29,30,31]).…”

Section: Introduction Motivation and Main Aimsmentioning

confidence: 99%

Localization of Fréchet frames and expansion of generalized functions

Pilipović¹,

Stoeva²

2019

Preprint

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Matrix type operators with the off-diagonal decay of polynomial or sub-exponential types are revisited with weaker assumptions concerning row or column estimates, still giving the continuity results for the frame type operators. Such results are extended from Banach to Fréchet spaces. Moreover, the localization of Fréchet frames is used for the frame expansions of tempered distributions and a class of Beurling ultradistributions.

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Section: Introduction Motivation and Main Aimsmentioning

confidence: 99%

Localization of Fréchet frames and expansion of generalized functions

Pilipović¹,

Stoeva²

2019

Preprint

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Localization of Fréchet Frames and Expansion of Generalized Functions

Pilipović

Stoeva

2021

Bull. Malays. Math. Sci. Soc.

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Matrix-type operators with the off-diagonal decay of polynomial or sub-exponential types are revisited with weaker assumptions concerning row or column estimates, still giving the continuity results for the frame type operators. Such results are extended from Banach to Fréchet spaces. Moreover, the localization of Fréchet frames is used for the frame expansions of tempered distributions and a class of Beurling ultradistributions.

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Fréchet Frames, General Definition and Expansions

Pilipović

Stoeva

2014

Anal. Appl.

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We define an (X1, Θ, X2)-frame with Banach spaces X2 ⊆ X1, · 1 ≤ · 2 , and a BK-space (Θ, |· |). Then by the use of decreasing sequences of Banach spaces {Xs} ∞ s=0 and of sequence spaces {Θs} ∞ s=0 , we define a general Fréchet frame on the Fréchet space XF = ∞ s=0 Xs. We give frame expansions of elements of XF and its dual X * F , as well of some of the generating spaces of XF with convergence in appropriate norms. Moreover, we give necessary and sufficient conditions for a general pre-Fréchet frame to be a general Fréchet frame, as well as for the complementedness of the range of the analysis operator U : XF → ΘF .

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Analysis of conditions for frame functions, examples with the orthogonal functions

Abstract: We analyze the construction of a sequence space Θ, resp. a sequence of sequence spaces, in order to haveas a Θ-frame or Banach frame for a Banach space X, resp. pre-F -frame or F -frame for a Fréchet space X F = ∩ s∈N0 X s , where {X s } s∈N0 is a sequence of Banach spaces.

Cited by 3 publications

References 10 publications

Localization of Fréchet frames and expansion of generalized functions

Localization of Fréchet frames and expansion of generalized functions

Localization of Fréchet Frames and Expansion of Generalized Functions

Fréchet Frames, General Definition and Expansions

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