Holomorphic Spaces Related to Orthogonal Polynomials and Analytic Continuation of Functions

  • Dmitri Karp
Part of the International Society for Analysis, Applications and Computation book series (ISAA, volume 9)


We prove three analytic continuation criteria for functions defined on the whole real line, positive half-line and a finite interval. The extended functions belong to certain reproducing kernel holomorphic spaces. The distinctive feature of our theorems is that no smoothness properties of functions to be extended are assumed in the hypotheses. Incidentally, new orthogonality properties of the Hermite and Laguerre polynomials and necessary and sufficient conditions for square summability with geometric weight θ k of the coefficients in these polynomials are proved.


Entire Function Analytic Continuation Orthogonal Polynomial Hermite Polynomial Laguerre Polynomial 


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© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • Dmitri Karp
    • 1
  1. 1.Department of MathematicsFar Eastern Academy of Economics and ManagementVladivostokRussia

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