عنوان

نظریه قاب وخواص آنهاروی فضاهای باناخ

Number

‭۵۷۳۲پ‬

.Language of Text, Soundtrack etc

per

Title Proper

نظریه قاب وخواص آنهاروی فضاهای باناخ

First Statement of Responsibility

/محمدرضا عبداله پور

Name of Publisher, Distributor, etc.

تبریز : دانشگاه تبریز ، دانشکده ریاضی، گروه ریاضی محض - آنالیز

Specific Material Designation and Extent of Item

‮‭۱۰۳‬ ص‬

Text of Note

چاپی

Text of Note

فاقد چکیده فارسی

Dissertation or thesis details and type of degree

دکتری

Discipline of degree

ریاضی محض - آنالیز

Date of degree

‮‭۱۳۸۶/۰۸/۲۵‬

Body granting the degree

تبریز : دانشگاه تبریز ، دانشکده ریاضی، گروه ریاضی محض - آنالیز

Text of Note

.‮‭In chapter (۱), we review the history of the frame theory and give some necessary definitions and theorems about different kinds of frames. In chapter (۲), we introduce the concept of pg-frames and g-Banach frames for banach spaces, and qg-Riesz bases for dual of Banach spaces. Pg-frame is a simultaneous generalization of pframe and g-frames. We show that by using of pg-frames a bounded linear functional on a Banach space can be represented as a unconditional convergent series. We also show that every separable Banach space has a g-Banach frame with bounds equal to ۱. In chapter (۳), by introducing the continuous g-frames, we try to find equivalent conditions for Riesz type continuous g-frames. We prove that under some conditions one can remove an element of a continuous g-frame such that the remaining set is also a continuous g-frame. In chapter (۴), we introduce an invariant analytic orthonormalization procedure and use this procedure to obtain orthonormal sets via frames of translates and Gabor frames‬

frame

Bessel sequence

synthesis and analysis operator

perturbation

continuous frame

frame of translates

Gabor frame

g-frame

pg-frame

qg-Riesz basis

g-banach frame

g-continuous frame

Riesz type

orthonormalization procedure

عبداله پور، محمد رضا

فاروقی، محمدد حسن، استادراهنما

سیفلو، حسین، استادمشاور

Public note

سیاه و سفید

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