Valićne karakterizacije Soboljevljevih prostora

master's thesis

• Author: Mario Stipčić
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Vjekoslav Kovač (predsjednik povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Committee member: Damir Bakić (član povjerenstva)
• Committee member: Zvonko Čerin (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj rad bavi se dokazima karakterizacije nehomogenih i homogenih Soboljevljevih prostora izražene preko koeficijenata funkcije ili općenitije distribucije u prikladnoj valićnoj bazi. Uz uvođenje pojmova valićne baze i Soboljevljevih prostora definiraju se još neki osnovni objekti te navode rezultati i dokazi potrebni za rad. Navodi se iskaz i dokaz karakterizacije Lebesgueovog prostora \(L^p (\mathbb{R}^n)\). Uz taj rezultat dokazuju se karakterizacije nehomogenog Soboljevljevog prostora \(W^{p,s} (\mathbb{R}^n)\) izražene preko koeficijenata dva tipa valićnih sistema, a zatim i karakterizacija homogenog Soboljevljevog prostora \(\mathring{W}^{p,s} (\mathbb{R}^n)\).

Abstract (english)

This thesis deals with the proofs of characterizations of inhomogeneous and homogeneous Sobolev spaces expressed through the coefficients of a function, or in general a distribution, in an appropriate wavelet basis. Along with the introduction of notions of a wavelet basis and Sobolev spaces, some other basic objects are defined and the results and proofs needed in the thesis are given. The statement and the proof of the characterization of the Lebesgue space \(L^p (\mathbb{R}^n)\) is given. Along with that result the characterizations of inhomogeneous Sobolev space \(W^{p,s} (\mathbb{R}^n)\) expressed through coefficients in two types of wavelet systems are established and then also the characterization of the homogeneous Sobolev space \(\mathring{W}^{p,s} (\mathbb{R}^n)\) is given.

• Keywords: karakterizacija nehomogenih Soboljevljevih prostora; karakterizacija homogenih Soboljevljevih prostora; valićna baza; karakterizacija Lebesgueovog prostora
• Keywords (english): characterizations of inhomogeneous Sobolev spaces; characterizations of homogeneous Sobolev spaces; wavelet basis; characterization of the Lebesgue space
• Language: croatian
• URN:NBN: urn:nbn:hr:217:073161
• Study programme: Title: Pure Mathematics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-07 12:31:08