Search results for "Rieszin energia"

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Äärellisten Borel-mittojen Fourier-muunnoksista euklidisissa avaruuksissa

2016

Tutkielmassa esitellään euklidisen avaruuden äärellisille Borel-mitoille Fourier-muunnokset kompleksiarvoisina kuvauksina ja tutkitaan niiden vähenemistä mentäessä ääarettömän kauas origosta. Keskeisenä kysymyksenä on, millä reunaehdoilla annetun kompkatikantajaisen ja äärellisen Borel-mitan Fourier muunnos vähenee polynomiaalisesti (eli sitä voidaan dominoida jollain euklidisen normin negatiivisella potenssilla) kaikkialla riittävän kaukana tai ainakin ”keskimääräisesti”. Mikäli tällainen Borel-mitta on absoluuttisesti jatkuva Lebesguen mitan suhteen kompaktikantajaisella ja sileällä tiheysfunktiolla, niin sen Fourier-muunnos vähenee aina polynomiaalisesti kaikkialla. Ongelmaa tarkastellaa…

Gaussin kuvauskapasitiivinen dimensioFourier-muunnospolynomiaalinen väheneminenFrostmanin lemmaRuellen siirto-operaattorisymbolinen dynamiikkaäärellinen Borel-mittaRieszin energiaGibbsin mittaRajchman-mitta

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