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A generalization of the Beurling—Lax theorem

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Abstract

We obtain conditions for the completeness of the system {G(z)e τz, τ ≤ 0} in the space H 2σ (ℂ+), 0 < σ < + ∞, of functions analytic in the right-hand half-plane for which

$$\parallel f\parallel : = \mathop {\sup }\limits_{ - \pi /2 < \varphi < \pi /2} \left\{ {\int_0^{ + \infty } {|f(re^{i\varphi } )|^2 } e^{ - 2r\sigma |\sin \varphi |} dr} \right\}^{1/2} < + \infty $$

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Authors and Affiliations

  1. I. Franko Drogobych Pedagogical University, Ukraine

    B. V. Vinnitskii & V. N. Dil’nyi

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  1. B. V. Vinnitskii
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  2. V. N. Dil’nyi
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__________

Translated from Matematicheskie Zametki, vol. 79, no. 3, 2006, pp. 362–368.

Original Russian Text Copyright ©2006 by B. V. Vinnitskii, V. N. Dil’nyi.

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Vinnitskii, B.V., Dil’nyi, V.N. A generalization of the Beurling—Lax theorem. Math Notes 79, 335–341 (2006). https://doi.org/10.1007/s11006-006-0038-2

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  • DOI: https://doi.org/10.1007/s11006-006-0038-2

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