SIMILAR TRANSFORMATION OF ONE CLASS OF WELL-DEFINED RESTRICTIONS

Biyarov B.N.
2025 L.N. Gumilyov Eurasian National University

Eurasian Mathematical Journal
2025 #16 Issue 1 8 - 21 pp.

In this paper there is considered the description of all well-defined restrictions of a maximal operator in a Hilbert space. A class of well-defined restrictions is found for which a similar transformation has the domain of the fixed well-defined restriction. The resulting theorem is applied to the study of n-order differentiation operator and the Laplace operator.

maximal (minimal) operator , Riesz basis with brackets , similar operators , singular coefficients , well-defined extension , well-defined restriction

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Institute of Mathematics and Mathematical Modeling, National Academy of Sciences of the Republic of Kazakhstan, 28 Shevchenko St., Almaty, 050010, Kazakhstan

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