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An approach to the solution of equations of the first kind with symmetric operators of Fredholm type

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Literature cited

  1. A. N. Tikhonov and V. Ya. Arsenin, Methods of Solving Improper Problems [in Russian], Nauka, Moscow (1974).

    Google Scholar 

  2. Yu. M. Berezanskii, Expansions in Eigenfunctions of Selfadjoint Operators, Amer. Math. Soc. (1968).

  3. L. Gårding, The Cauchy Problem for Hyperbolic Equations [Russian translation], IL, Moscow (1961).

    Google Scholar 

  4. V. P. Didenko and I. I. Lyashko, Dynamical Systems with Discontinuous Characteristics [in Russian], Kiev Univ. (1977).

  5. I. I. Lyashko, V. P. Didenko, and O. E. Tsitritskii, “Filtration with colored noise in the observations,” Dokl. Akad. Nauk SSSR,238, No. 5, 1051–1054 (1978).

    Google Scholar 

  6. I. I. Lyashko, V. P. Didenko, and V. I. Garkusha,” On equations of the first kind and Riccati equations depending on a parameter,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 1125–1128 (1977).

    Google Scholar 

  7. I. I. Lyashko and V. P. Didenko, “On Tikhonov regularizations of problems with symmetric operators in Hilbert spaces,” Dokl. Akad. Nauk SSSR,226, No. 3, 510–512 (1976).

    Google Scholar 

  8. V. P. Didenko and N. N. Kozlov, “On regularizations of some improper problems of technical cybernetics,” Dokl. Akad. Nauk SSSR,214, No. 3, 528–530 (1974).

    Google Scholar 

  9. I. I. Gihman and A. V. Skorokhod, The Theory of Stochastic Processes, Springer-Verlag (1975).

  10. H. Kwakernaak and R. Sivan, Linear Optimal Control Systems, Wiley (1972).

  11. K. Ostrem, Introduction to the Theory of Stochastic Control [Russian translation], Mir, Moscow (1973).

    Google Scholar 

  12. T. Kailath, “Fredholm resolvents, Wiener-Hopf equations, and Riccati differential equations,” IEEE Trans. Inf. Theory,IT-15, No. 6, 665–672 (1969).

    Google Scholar 

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol.31, No. 6, pp. 666–674, November–December, 1979.

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Garkusha, V.I. An approach to the solution of equations of the first kind with symmetric operators of Fredholm type. Ukr Math J 31, 513–520 (1979). https://doi.org/10.1007/BF01092531

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  • DOI: https://doi.org/10.1007/BF01092531

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