Composite wavelet transforms: Applications and perspectives

ALİYEV İ., Rubin B., Sezer S., Uyhan S.

Special Session on Radon Transforms, Geometry, and Wavelets held at the AMS Annual Meeting, Louisiana, Amerika Birleşik Devletleri, 7 - 08 Ocak 2007, cilt.464, ss.1-4 identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 464
  • Basıldığı Şehir: Louisiana
  • Basıldığı Ülke: Amerika Birleşik Devletleri
  • Sayfa Sayıları: ss.1-4
  • Anahtar Kelimeler: wavelet transforms, potentials, semigroups, generalized translation, Radon transforms, inversion formulas, matrix spaces, BESSEL POTENTIALS, PARABOLIC POTENTIALS, RADON TRANSFORMS, GENERALIZED TRANSLATION, RIDGELET TRANSFORMS, LIPSCHITZ SPACES, LEBESGUE SPACES, INVERSION, INTEGRALS, MATRICES
  • Akdeniz Üniversitesi Adresli: Evet

Özet

We introduce a new concept of the so-called composite wavelet transforms. These transforms are generated by two components, namely, a kernel function and a wavelet function (or a measure). The composite wavelet transforms and the relevant Calderon-type reproducing formulas constitute a unified approach to explicit inversion of the Riesz, Bessel, Flett, parabolic and some other operators of the potential type generated by ordinary (Euclidean) and generalized (Bessel) translations. This approach is exhibited in the paper. Another concern is application of the composite wavelet transforms to explicit inversion of the k-plane Radon transform on R-n. We also discuss in detail a series of open problems arising in wavelet analysis of L-p-functions of matrix argument.