Banach Journal of Mathematical Analysis

Exponential Monomials on Sturm--Liouville Hypergroups

Laszlo Vajday

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Abstract

Using the concept of exponential monomial on Sturm--Liouville hypergroups we show that an important subclass of exponential monomials, the class of special exponential monomials has a linear independence property. The result can be reformulated as the linear independence of the derivatives with respect to the parameter of the solutions of eigenvalue problems for second order linear differential equations.

Article information

Source
Banach J. Math. Anal., Volume 4, Number 2 (2010), 139-146.

Dates
First available in Project Euclid: 7 February 2011

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1297117248

Digital Object Identifier
doi:10.15352/bjma/1297117248

Mathematical Reviews number (MathSciNet)
MR2610885

Zentralblatt MATH identifier
1191.43006

Subjects
Primary: 39B82: Stability, separation, extension, and related topics [See also 46A22]
Secondary: 44B20 46C05: Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)

Keywords
spectral analysis spectral synthesis hypergroups

Citation

Vajday, Laszlo. Exponential Monomials on Sturm--Liouville Hypergroups. Banach J. Math. Anal. 4 (2010), no. 2, 139--146. doi:10.15352/bjma/1297117248. https://projecteuclid.org/euclid.bjma/1297117248


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References

  • W.R. Bloom and H. Heyer, Harmonic Analysis of Probability Measures on Hypergroups, de Gruyter Studies in Mathematics, de Gruyter, Berlin, New York, 1995.
  • L. Székelyhidi, Spectral Analysis and Spectral Synthesis on Polynomial Hypergroups, Monatsh. Math. 141 (2004), no. 1, 33–43.
  • L. Székelyhidi, Spectral Synthesis on Multivariate Polynomial Hypergroups, Monatsh. Math. 153 (2008), no. 2, 145–152.