Abstract
We derive an expansion of a holomorphic function in terms of totally positive polynomials and interpret the result as an orthogonal expansion in a Krein space. As a special case, expansions in terms of Bessel polynomials are considered.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Arms, R.J. and Edrei, A., The Padé tables and continued fractions generated by totally positive sequences, Mathematical Essays dedicated to A.J. Macintyre, 1–21. Ohio Univ. Press, Athens, Ohio (1970).
Baker, G.A., Essentials of Padé Approximants, Acad. Press, New York (1975).
Bognar, J., Indefinite inner product spaces, Springer, Berlin (1974).
Bruin, M.G. de, Convergence in the Padé table for lFl(l;c;x). Kon. Ned. Akad. v. Wet. Ser A, 79, no 5 = Indag. Math., 38, no 5, 408–418 (1976).
Edrei, A., Proof of a conjecture of Schoenberg on the generating function of a totally positive sequence, Can. Journ. of Math., 5, 86–94 (1953).
Krall, H.L. and Frink, O.A., A new class of orthogonal polynomials: the Bessel polynomials, Trans. Am. Math. Soc., 65, 100–115 (1949).
Nassif, M., Note on the Bessel polynomials, Trans. Am. Math. Soc., 77, 408–412 (1954).
Rossum, H. van, Totally positive polynomials, Kon. Ned. Akad. v. Wet. Ser A, 68 no 2 = Indag. Math., 27, no 2 (1965).
Rossum, H. van, A theory of orthogonal polynomials based on the Padé table, Thesis, Van Gorcum, Assen (1953).
Rossum, H. van, Padé approximants and indefinite inner product spaces, in: Padé and rational approximation, Theory and applications, Ed. E.B. Saff and R.S. Varga, Tampa, (1976).
Whittaker, J.M., Sur les séries de base de polynomes quelconques, Gauthier-Villars, Paris, (1949).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag
About this paper
Cite this paper
van Rossum, H. (1979). Orthogonal expansions in indefinite inner product spaces. In: Wuytack, L. (eds) Padé Approximation and its Applications. Lecture Notes in Mathematics, vol 765. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0085580
Download citation
DOI: https://doi.org/10.1007/BFb0085580
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09717-4
Online ISBN: 978-3-540-38511-0
eBook Packages: Springer Book Archive