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Статья
2014

The structure of the resolvent for the discrete renewal equation with nonsummable difference kernel


I. L. OinasI. L. Oinas, T. A. SivachevaT. A. Sivacheva, Z. B. TsalyukZ. B. Tsalyuk
Русская математика
https://doi.org/10.3103/S1066369X1405003X
Abstract / Full Text

We find the asymptotic structure of the resolvent for the various cases of zeros of symbol for the discrete difference renewal equations with the nonsummable kernel.

Author information
  • Kuban State University, ul. Stavropol’skaya 149, Krasnodar, 350040, RussiaI. L. Oinas, T. A. Sivacheva & Z. B. Tsalyuk
References
  1. I. L. Oinas and Z. B. Tsalyuk, “The Asymptotic Character of the Resolvent of Discrete Equation in Convolutions,” Available from VINITI, No. 3127-B98 (Kuban State University, 1998).
  2. I. L. Oinas, “The Asymptotic Behavior of the Resolvent of Discrete Equation of Convolution Type in an Unstable Case,” Available from VINITI, No. 2636-B99 (Kuban State University, 1999).
  3. I. L. Oinas, “The Asymptotic Structure of the Resolvent for Some Class of Kernels of a Difference Equation,” Available from VINITI, No. 517-B2004 (Kuban State University, 2004).
  4. Z. B. Tsalyuk and M. B. Tsalyuk, “The Resolvent Structure of a Volterra Equation with Nonsummable Difference Kernel,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 4, 72–82 (2010) [Russian Mathematics (Iz. VUZ) 54 (4), 62–71 (2010)].
  5. G.M. Fikhtengolts, Course of Differential and Integral Calculus (Nauka, Moscow, 1962), Vol. 2.
  6. W. Feller, An Introduction to Probability Theory and its Applications (John Wiley & Sons, New York, 1950; Mir, Moscow, 1967), Vol. 1.