Okviri i translaciono invarijantni prostori

Simić, Suzana

Frames and translation invariant spaces

Abstract

U disertaciji se daje pregled osnovnih pojmova i poznatih rezultata teorije okvira. Prou·cavani su translaciono inavarijantni prostori sa te·zinama i dati uslovi pod kojima kolekcija funkcija ·cini okvir u tom prostoru. Takod¹e, konstruisan je niz takvih prostora i prikazani uslovi pod kojima ¶ce odgovaraju¶ce funkcije koje generi·su taj prostor predstavljati ili Banach-ov okvir ili Riesz-ovu bazu, i samim tim ustanoviti zatvorenost takvog prostora.

The basic notions and known results from the theory of frames are given in thesis. We study translation-invariant weighted spaces and give the conditions for a collection of functions to form a frame. Further, we construct a sequence of such spaces and show when the appropriate chosen functions form a p-frame or Riesz basis, and according to that explain the closedness of the space generated with these functions.

Faculty:
University of Novi Sad, Faculty of Science
Date:
03-12-2011

Keywords:

Prostori distribucija, p-okvir, te·zinski prostori, translaciono in- varijantni prostori, Fr¶echet-ov okvir / Space of distributions, p-frame, weighted spaces, transla- tion-invariant spaces, Fr¶echet-frame

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