### MATHEMATICAL BASES OF OPTIMAL MEASUREMENTS THEORY IN NONSTATIONARY CASE

#### Abstract

Recently, the use of mathematical results is becoming increasingly vast field of study for solving technical problems. An example of such approach is the recently developed optimal measurement theory. In the article the mathematical reasoning for solution of the measurement problem of dynamically distorted signal, taking into account the multiplier effect on the measuring transducer (MT). Making such a~change can improve the adequacy of the mathematical model of the MT, namely, the problem is considered under the assumption that the MT are subject to change over time, which allows us to describe a~decrease in sensitivity of elements of the MT.

#### Keywords

nonstationary Sobolev type equations, relatively bounded operator, degenerate flow of operators, optimal control problem, Showalter--Sidorov problem.

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