270 KB9154 KB92 KB1971Tomšič, GabrijelVidav, Ivan79 f., 30 cm82 straniCOBISSID:6099717URN:URN:NBN:SI:doc-1ZDQEO83slG. Tomšičvisokošolska delahomogene spektralne merehomogeni operatorjikvaziinvariantne mereteorija operatorjevurejena reprezentacijaurejena reprezentacija za spektralne mereHomogeni operatorji in homogene spektralne mere| doktorska disertacija|A self adjoint operator ?$A$? defined on a separable Hilbert space is called homogeneous if, for every real ?$\lambda$?, the operator ?$A - \lambda I$? is unitarily equivalent to ?$A$?. Unitary operator ?$U$? on separable Hilbert space is called homogeneous if for each ?$\alpha$?, ?$0 \le \alpha \le 2\pi$?, the operator ?$e^{i\alpha}U$? is unitarily equivalent to ?$U$?. A characterization for homogeneous operators is given. Homogeneous spectral measure ?$E(e)$? on a separable Hilbert space is called homogeneous for every translation ?$\tau$? and every Borel set ?$e$?, if the spectral measure ?$E(\tau e)$? is equivalent to ?$E(e)$?. A characterization for homogeneous spectral measures is givenSebi adjungiran operator ?$A$? definiran na separabilnem Hilbertovem prostoru je homogen, če je za vsak realen ?$\lambda$? operator ?$A - \lambda I$? unitarno ekvivalenten operatorju ?$A$?. Unitaren operator ?$U$? je homogen, če je ekvivalenten operatorju ?$e^{i\alpha}U$? za vsak ?$\alpha$?, ?$0 \le \alpha \le 2\pi$?. Spektralna mera ?$E(e)$? na separabilnem Hilbertovem prostoru je homogena za translacijo ?$\tau$? in za vsako Borelovo množico ?$e$?, če je spektralna mera ?$E(\tau e)$? ekvivalentna meri ?$E(e)$?. Namen naloge je dobiti karakterizacijo za homogene operatorje in za homogene spektralne meredoktorska disertacijaTEXTvisokošolska delatheses and dissertationsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza v Ljubljani, Fakulteta za matematiko in fiziko