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Realization of entire operators by differential ones

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Abstract

In this paper, it is shown that the minimal operator generated by a second order operator differential expression of hyperbolic type is entire. As the coefficients of the equation are in general unbounded operators, it covers a number of partial differential equations. In this way the problem of realization of entire operators by partial differential ones as originally introduced by M. G. Krein in 1966 is solved. For the minimal operator, it is given also the analytical description of all its spectral functions. This paper is dedicated to memory of M. G. Krein who was a founder of the theory of entire operators.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, 47B25, 34G10, Kyiv

    M. L. Gorbachuk & V. I. Gorbachuk

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  1. M. L. Gorbachuk
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  2. V. I. Gorbachuk
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Partially supported by INTAS-93-0249-ext.

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Gorbachuk, M.L., Gorbachuk, V.I. Realization of entire operators by differential ones. Integr equ oper theory 30, 200–230 (1998). https://doi.org/10.1007/BF01238219

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  • DOI: https://doi.org/10.1007/BF01238219

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