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 the article). The purpose of this paper is to study the system of fundamental functions of the equation. We will carry out the reasoning 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. Doklady AN SSSR, 6, 1950, LXXH. (in Russian)
- Nomokonov M.K. On the spectrum of one class of integral equations with a stochastic kernel. Doklady AN SSSR, 1952, LXXXIV, 3. (in Russian)
- Sarmanov O.V. On monotone solutions of correlation integral equations. Doklady AN SSSR, 1946, LIII, 9. (in Russian)
- Sarmanov O.V. On the straightening of asymmetric correlation. Doklady AN SSSR, 1948, L1X, 5. (in Russian)
- Iench R. Uber Integralgleichungen mit positivem Kern. Journal f. reine u. ang. 1912, M. 141, H. 4. 235—244.
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