Petr Zabreiko

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The existence of the second (according to the module) eigenvalue λ2 of a completely continuous nonnegative operator A is proved under the conditions that A acts in the space Lp(Ω) or C(Ω) and its exterior square A∧A is also nonnegative. For the case when the operators A and A∧A are indecomposable, the simplicity of the first and second eigenvalues is(More)
The paper is devoted to the calculation of the index of a zero and the asymptotic index of a linear completely continuous nonnegative operator. Also the case of a nonlinear completely continuous operator A whose domain and image are situated in a closed convex set Q of a Banach space is considered. For this case, we formulate the rules for calculating the(More)
The tensor and exterior squares of a completely continuous non-negative linear operator A acting in the ideal space X(Ω) are studied. The theorem representing the point spectrum (except, probably, zero) of the tensor square A ⊗ A in the terms of the spectrum of the initial operator A is proved. The existence of the second (according to the module) positive(More)
1 ] A. Rosenfeld and A. Kak, Digital Picture Processing. New York: Academic, 1976. [21 B. Lipkin and A. Rosenfeld, Picture Processing and Psychopictorics. New York: Academic, 1970. [31 W. Pratt, Digital Image Processing. New York: Wiley, 1978. [41 M. Krasnoselsky, A. Perov, and P. Zabreiko, Plane Vector Fields. New York: Academic, 1961. [5] J. Milnor,(More)
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