Some Spectral Properties of Multiplicative Hermite Equation - Göktaş, Sertaç; Yılmaz, Emrah; Yar, Ayşe Çiğdem (My University, 2022)
We reconstruct the Multiplicative Hermite Equation from multiplicative Sturm-Liouville equation. A new representation of eigenfunctions for the constructed problem are obtained by the power series solution technique. While making these solutions, multiplicative Hermite polynomials were used strongly. We get a generator for multiplicative Hermite polynomials and construct integration representations for these polynomials. Finally, some spectral properties of the multiplicative Hermite problem are examined in detail.
Keywords: Hermite equation; Multiplicative calculus; Multiplicative Sturm-Liouville equation