L{sub 2}-stable semigroups, Muckenhoupt weights, and unconditional bases of values of quasi-exponentials

Journal Article · Fri Dec 31 04:00:00 EST 1999 · Sbornik. Mathematics

DOI:https://doi.org/10.1070/SM1999V190N12ABEH000442; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)· OSTI ID:21202899

Gubreev, G M ^[1]

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1. South Ukrainian State K.D.Ushynsky Pedagogical University, Odessa (Ukraine)

A class of unbounded operators with discrete spectrum in a separable Hilbert space is distinguished, in which the property of being the generator of an L{sub 2}-stable semigroup is equivalent to the similarity to the Sz.-Nadya-Foiash scalar model. In the proof of this result a connection with the theory of Muckenhoupt weights is established. A criterion for the similarity of a dissipative unicellular operator to the simplest integration operator is also derived. The notion of a quasiexponential, an abstract analogue of an exponential, is introduced. As an application, a description of all unconditional bases in the Hilbert space consisting of values of a quasiexponential is presented.

• OSTI ID: 21202899
• Journal Information: Sbornik. Mathematics, Journal Name: Sbornik. Mathematics Journal Issue: 12 Vol. 190; ISSN 1064-5616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
HILBERT SPACE
SCALARS
SPECTRA
WEIGHT