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- W951657060 abstract "A palyazat soran a kutatasi programnak megfelelő teruleteken osszesen 31 tudomanyos publikacio szuletett. A palyazat egyik resztvevője 2005-ben vedte meg sikeresen Akademiai Doktori Ertekezeset a palyazati tervben szereplő kutatasi temaban. A program soran vegzett elmeleti kutatasok teremtettek meg az alapot ket alkalmazott, orvos biologiai projektbe valo bekapcsolodashoz is. Az ortogonalis sorok szummacioja teren szamos uj eredmenyt igazoltunk, peldaul Walsh, Walsh-Kaczmarcz, Vilenkin, Ciesielski rendszerekre vonatkozo Theta-szummacio konvergenciajara vonatozoan, valamint a Gabor analizisben tobb eddig nem vizsgalt ter eseten is. Multiplier operatorokkal kapcsolatban a Hormander-Mihlin-fele multiplier operatorok korlatossagat igazoltuk Hardy terekben a klasszikus es a diadikus esetre, utobbira tobb dimenzioban is. Az adott problemahoz illeszkedő ortogonalis rendszer konstrualasanak problemakore kapcsan a Malmquist-Takenaka, a gombfuggvenyek es a Zernike rendszer teruleten ertunk el eredmenyeket. A matematikai fizikaban, a jel- es kepfeldolgozasban alkalmazott Gabor- es a wavelet transzformacionak egy kozos altalanositasa a voice transzformacio a. A racionalis fuggvenyek Blaschke-fele csoportjat felhasznalva bevezettunk a voice transzformacio 3 valtozatat, tisztaztuk a lekepezesek legfontosabb tulajdonsagait. | 31 publications were written in the fields specified in the scientific program during the project. One of the participants defended his Doctor of Science thesis in this period. Another product is that part of our results provided the theoretical basis for our participation in two applied medical projects. In the area of Theta summation processes we proved new theorems for several systems such as Walsh, Walsh-Kaczmarz, Ciesielski systems in different spaces. The same questions were investigated in Gabor analysis and in spaces that have not been considered before. We showed the boundedness of Hormander-Mihlin type multiplier operators in the classical and in the dyadic Hardy spaces, also in two dimensions for the latter one. Concerning the construction of adaptive orthogonal systems we proved new results for the Malmquist-Takenaka, the Zernike systems and for spherical functions. The voice transform is a generalization of both the Gabor and the wavelet transforms, which are used in mathematical physics, and in signal and image processing. By means of the Blaschke group of rational functions we defined three versions of the voice transform, and then characterized their main properties of these transforms." @default.
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- W951657060 date "2008-01-01" @default.
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- W951657060 title "Walsh és Walsh-szerű rendszerek vizsgálata = Analysis of Walsh and Walsh like systems" @default.
- W951657060 hasPublicationYear "2008" @default.
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