On correlation integral equations whose fundamental functions are polynomials
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Abstract
A correlation integral equation is an equation of the following form (see article). The purpose of this paper is to study the system of fundamental functions of the equation. The reasoning will be carried out for the case of symmetric correlation (see the article). However, this restriction can be easily removed and non-symmetric correlation can be considered if we pass to the system of integral equations using the Hilbert-Schmidt theory. Let us prove several theorems (see the article).
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References
- Nomokonov M.K. On the simplicity and sign of the second characteristic number of correlation integral equations. Reports of the AS USSR, 6, 1950, LXXH.
- Nomokonov M.K. On the spectrum of one class of integral equations with a stochastic kernel. Reports of the Academy of Sciences of the USSR, 1952, LXXXIV, 3.
- Sarmanov O.V. On monotone solutions of correlation integral equations. Reports of the AS USSR, 1946, LIII, 9.
- Sarmanov O.V. On the straightening of asymmetric correlation. Reports of the AS USSR, 1948, L1X, 5.
- Iench R. On integral equations with positive kernel. Journal for Pure and Applied Mathematics 1912, V. 141, iss. 4. pp. 235-244.
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