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- Title
Multipliers of the Hilbert spaces of Dirichlet series.
- Authors
Sahu, Chaman Kumar
- Abstract
For a sequence w = {wj}j=2∞ of positive real numbers, consider the positive semi-definite kernel kw(s,u) = ...defined on some right-half plane ... for a real number Ρ. Let Hw denote the reproducing kernel Hilbert space associated with KW. Let ... where [Pj}j≥1 is an increasing enumeration of prime numbers and gpf(n) denotes the greatest prime factor of an integer n ≥ 2. If w satisfies ... where µ is the Möbius function, then the multiplier algebra M(Hw of Hw is isometrically isomorphic to the space of all bounded and holomorphic functions on ... that are representable by a convergent Dirichlet series in some right half plane. As a consequence, we describe the multiplier algebra M(Hw) when w is an additive function satisfying δw ≤ 0 and ... for all integers j ≥ 2 and all prime numbers p. Moreover, we recover a result of Stetler that describes the multipliers of Hw when w is multiplicative. The proof of the main result is a refinement of the techniques of Stetler.
- Subjects
REAL numbers; PRIME numbers; MOBIUS function; ALGEBRA; HILBERT space; HOLOMORPHIC functions; DIRICHLET series; INTEGERS; ADDITIVE functions
- Publication
New York Journal of Mathematics, 2023, Vol 29, p323
- ISSN
1076-9803
- Publication type
Article