Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 2

Some relations satisfied by orthogonal matrix polynomials

Pages
241–253
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Further- more, for these matrix polynomials, we give raising operators.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials.
📊
Key Findings & Data:We derive identities for power series satisfied by Laguerre, Hermite and Gegenbauer matrix polynomials.
💡
Conclusion & Impact:Further- more, for these matrix polynomials, we give raising operators.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

The main purpose of this paper is to obtain some properties of orthog- onal matrix polynomials. We derive identities for power series satisfied by Laguerre, Hermite and Gegenbauer matrix polynomials. Further- more, for these matrix polynomials, we give raising operators.

🔖

Cite This Article

AKTAŞ, R., ÇEKİM, B., ALTIN, A. (2022). Some relations satisfied by orthogonal matrix polynomials. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 2, 241–253. https://ajindex.com/articles/530628

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (17)

  1. Batahan, R. S. A new extension of Hermite matrix polynomials and its applications, Linear Algebra and its Applications 419, 82–92, 2006
  2. Defez, E., Hervas, A., Law, A., Villanueva-Oller, J. and Villanueva, R. J. Progressive trans- mission of images: PC-based computations, using orthogonal matrix polynomials, Math. Comput. Modelling 32, 1125–1140, 2000
  3. Defez, E. and Jodar, L. Chebyshev matrix polynomials and second order matrix differential equations, Utilitas Mathematica 61, 107–123, 2002
  4. Defez, E. and Jodar, L. Some applications of the Hermite matrix polynomials series expan- sions, J. Comput. Appl. Math. 99, 105–117, 1998
  5. Defez, E., Jodar, L. and Law, A. Jacobi matrix differential equation, polynomial solutions and their properties, Computers and Mathematics with Applications 48, 789–803, 2004
  6. Defez, E., Jodar, L., Law, A. and Ponsoda, E. Three-term recurrences and matrix orthogonal polynomials, Utilitas Mathematica 57, 129–146, 2000
  7. Defez, E., Law, A., Villanueva-Oller, J. and Villanueva, R. J. Matrix cubic splines for pro- gressive 3D imaging, J. Math. Imag. and Vision 17, 41–53, 2002
  8. Dunford, N. and Schwartz, J. Linear Operators. Vol. I, (Interscience, New York, 1957)
  9. Duran, A. J. On orthogonal polynomials with respect to a positive definite matrix of mea- sures, Canadian J. Math. 47, 88–112, 1995
  10. Duran, A. J. and Lopez-Rodriguez, P. Orthogonal matrix polynomials: zeros and Blumen- thal’s theorem, J. Approx. Theory 84, 96–118, 1996
  11. Geronimo, J. S. Scattering theory and matrix orthogonal polynomials on the real line, Circuit Systems Signal Process 1 (3-4), 471–494, 1982
  12. James, A.T. Special functions of matrix and single argument in statistics, In Theory and Applications of Special Functions, Academic Press, (Edited by R.A. Askey), 497–520, 1975
  13. J´odar, L. and Company, R. Hermite matrix polynomials and second order matrix differential equations, J. Approx. Theory Appl. 12 (2), 20–30, 1996
  14. J´odar, L., Company, R. and Navarro, E. Laguerre matrix polynomials and system of second- order differential equations, Appl. Num. Math. 15, 53–63, 1994
  15. Jodar, L., Company, R. and Ponsoda, E. Orthogonal matrix polynomials and systems of second order differential equations, Differential Equations and Dynamical Systems 3, 269– 288, 1996
  16. Jodar, L. and Cortes, J.C. On the hypergeometric matrix function, J. Comput. Appl. Math. 99, 205-217, 1998
  17. Jodar, L. and Defez, E.A. Connection bet