Geodesic
$L_2$-stable semigroups, Muckenhoupt weights, and unconditional bases of values of quasi-exponentials
Sbornik. Mathematics, Tome 190 (1999) no. 12, pp. 1715-1747 Cet article a éte moissonné depuis la source Math-Net.Ru

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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 $L_2$-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. 
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G. M. Gubreev. $L_2$-stable semigroups, Muckenhoupt weights, and unconditional bases of values of quasi-exponentials. Sbornik. Mathematics, Tome 190 (1999) no. 12, pp. 1715-1747. http://geodesic.mathdoc.fr/item/SM_1999_190_12_a0/

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