Regular algebras of dimension 2, the generalized eigenvalue problem and Padé interpolation

References

• Artin M Schelter W F Graded algebras of global dimension 3, Advances in Math. 66 (1987), 171–216
   Google Scholar
• Atkinson F V Multiparameter Eigenvalue Problems, Academic Press, 1972
   Google Scholar
• Baker G A Graves-Morris P Padé approximants. Parts I and II., Encyclopedia of Mathematics and its Applications, 13, 14. Addison-Wesley Publishing Co., Reading, Mass., 1981
   Google Scholar
• Chihara T S An introduction to orthogonal polynomials, Mathematics and its Applications, Vol. 13, Gordon and Breach Science Publishers, New York-London-Paris, 1978
   Google Scholar
• Erdélyi A Magnus W Oberhettinger F Tricomi F Higher transcendental functions. Vols. I, II, Based, in part, on notes left by Harry Bateman, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1953
   Google Scholar
• Gantmaher F R The Theory of Matrices, vols. 1–2, Chelsea, NY, 1959
   Google Scholar
• Gasper G Rahman M Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990
   Google Scholar
• Irving R S Prime ideals of Ore extensions over commutative rings, II, J. Algebra 58 (1979), 399–423
   Google Scholar
• Iserles A Rational interpolation to exp(-x) with application to certain stiff systems. SIAM J. Numer. Anal. 18 (1981), 1–12
   Google Scholar
• Ismail M Masson D Generalized orthogonality and continued fractions, J. Approx. Theory 83 (1995), 1–40
   Google Scholar
• Koekoek R Swarttouw R The Askey-scheme of hypergeometric orthogonal polynomials and its q-analogue, Delft University of Technology, Faculty of Information Technology and Systems, Department of Technical Mathematics and Informatics, Report no. 98–17, 1998
   Google Scholar
• Meinguet J On the solubility of the Cauchy interpolation problem, Approximation Theory (Proc. Sympos., Lancaster, 1969), Academic Press, London, 1970, 137–163
   Google Scholar
• Rieffel M Quantum Deformations for Actions of Rd, Mem. Amer. Math. Soc. 506, American Mathematical Society, Providence, 1993
   Google Scholar
• Spiridonov V Zhedanov A Discrete-time Volterra chain and classical orthogonal polynomials, J. Phys. A 30 (1997), 8727–8737
   Google Scholar
• Spiridonov V Vinet L Zhedanov A Spectral transformations, self-similar reductions and orthogonal polynomials, J. Phys. A 30 (1997), 7621–7637
   Google Scholar
• Spiridonov V Zhedanov A Generalized eigenvalue problem and a new family of rational functions biorthogonal on elliptic grids, Special functions 2000, Kluwer, 2001, 365–388
   Google Scholar
• Spiridonov V Zhedanov A To the theory of biorthogonal rational functions, RIMS Proceedings, 2003
   Google Scholar
• Wilkinson J H The Algebraic Eigenvalue Problem, Clarendon Press, Oxford, 1965
   Google Scholar
• Zhedanov A S On the realization of the Weyl commutation relation HR=qRH, Phys. Lett. A 176 (1993), 300–302
   Google Scholar
• Zhedanov A Biorthogonal rational functions and the generalized eigenvalue problem, J. Approx. Theory 101 (1999), 303–329
   Google Scholar
• Zhedanov A Biorthogonality of the Lagrange interpolants, J. Comput. Appl. Math. 172 (2004), 1–6
   Google Scholar
• Zhedanov A Explicit multipoint rational interpolation Padé table for exponential and power functions, CRM Proceedings and Lecture Notes 39 (2004), 285–298
   Google Scholar
• A. Zhedanov, Padé interpolation table and biorthogonal rational functions, Proceedings of RIMS Workshop on Elliptic Integrable Systems, Kyoto, November 8–11, 2004, to be published. http://www.math.sci.kobe-u.ac.jp/HOME/noumi/EIS/zhedanov4.pdf
   Google Scholar