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

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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. 
@article{SM_1999_190_12_a0,
     author = {G. M. Gubreev},
     title = {$L_2$-stable semigroups, {Muckenhoupt} weights, and unconditional bases of values of quasi-exponentials},
     journal = {Sbornik. Mathematics},
     pages = {1715--1747},
     publisher = {mathdoc},
     volume = {190},
     number = {12},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_12_a0/}
}
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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/