Fourier Transforms of Orthogonal Structures on the Paraboloid

Özkan Çetin H., AKTAŞ KARAMAN R.

Mediterranean Journal of Mathematics, cilt.23, sa.3, 2026 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 23 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s00009-026-03086-3
  • Dergi Adı: Mediterranean Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, DIALNET
  • Anahtar Kelimeler: contiguous relation, Fourier transform, Hahn polynomials, hypergeometric function, Jacobi polynomials, Laguerre polynomials, multivariate orthogonal polynomials, Parseval’s identity
  • Ankara Üniversitesi Adresli: Evet

Özet

The purpose of this paper is to obtain Fourier transforms of multivariate orthogonal structures on the paraboloid such as Laguerre polynomials on the paraboloid and Jacobi polynomials on the paraboloid, and to define two new families of multivariate orthogonal functions by using Parseval’s identity. In addition, some contiguous relations for these families of functions are given and the obtained results are expressed in terms of the continuous Hahn polynomials. Finally, we provide graphical illustrations of some special functions and their Fourier transforms.