7 Hardy - type theorem for orthogonal functions with respect to their zeros . The Jacobi weight case
نویسندگان
چکیده
Motivated by G. H. Hardy's 1939 results [4] on functions orthogonal with respect to their real zeros λn, n = 1, 2,. .. , we will consider, within the same general conditions imposed by Hardy, functions satisfying an orthog-onality with respect to their zeros with Jacobi weights on the interval (0, 1), that is, the functions f (z) = z ν F (z), ν ∈ R, where F is entire and Z 1 0 f (λnt)f (λmt)t α (1 − t) β dt = 0, α > −1 − 2ν, β > −1, when n = m. Considering all possible functions on this class we are lead to the discovery of a new family of generalized Bessel functions including Bessel and Hyperbessel functions as special cases.
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