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- W2008296438 abstract "Let K be a complex valued measurable function on (0, 1] such that fXI t-11 IK(t)l dtisfinite forsomep>1. Let Hbe the Hausdorff operator on I determined by the moments yi,,= j o t?K(t) dt. Define 'V(z)= j tzK(t) dt. Then for each z with Re z> -I/p, 'I'(z) is an eigenvalue of Hf*. The spectrum of H is the union of {O} with the range of T on the half-plane Re z_-I/p. If Iu is a complex Borel measure concentrated on (0, 1] and satisfying G t-11' dUll(t) lIp) to the general class of operators H corresponding to absolutely continuous measures ,u. Our theorem expresses the spectrum as the compactified range of the Mellin transform of tll d,u(t) over the half-plane Im s>0. Throughout, p is a real number greater than one. It is shown in [3] that for each complex number 2 such that Re i%1> l/q, the sequence g, defined by the generating function" @default.
- W2008296438 created "2016-06-24" @default.
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- W2008296438 date "1973-03-01" @default.
- W2008296438 modified "2023-09-24" @default.
- W2008296438 title "Discrete Hausdorff transformations" @default.
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- W2008296438 doi "https://doi.org/10.1090/s0002-9939-1973-0315508-0" @default.
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