Direct and Inverse Problems of Spectral Analysis for Arbitrary-Order Differential Operators with Nonintegrable Regular Singularities

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Abstract

A short review is presented of results on the spectral theory of arbitrary order ordinary differential operators with non-integrable regular singularities. We establish properties of spectral characteristics, prove theorems on completeness of root functions in the corresponding spaces, prove expansion and equiconvergence theorems, and provide a solution of the inverse spectral problem for this class of operators.

About the authors

V. A. Yurko

Chernyshevskii Saratov National Research State University

Author for correspondence.
Email: yurkova@info.sgu.ru
Saratov, Russia

References

  1. Вазов В. Асимптотические разложения решений обыкновенных дифференциальных уравнений. - М.: Мир, 1968.
  2. Костюченко А. Г., Саргсян И. С. Распределение собственных значений. Самосопряженные обыкновенные дифференциальные операторы. - М.: Наука, 1979.
  3. Наймарк М. А. Линейные дифференциальные операторы. - М.: Наука, 1969.
  4. Юрко В. А. О дифференциальных операторах высших порядков с регулярной особенностью// Мат. сб. - 1995. - 186, № 6. - С. 133-160.
  5. Юрко В. А. Введение в теорию обратных спектральных задач. - М.: Физматлит, 2007.
  6. Ignatiev M. Yu. Integral transforms connected with differential systems with a singularity// Tamkang J. Math. - 2019. - 50, № 3. - С. 253-268.
  7. Ignatiev M. Yu. Asymptotics of solutions of some integral equations connected with differential systems with a singularity// Изв. Саратов. ун-та. Нов. сер. Сер. Мат. Мех. Инф. - 2020. - 20, № 1. - С. 17-28.
  8. Turrittin H. Stokes multipliers for asymptotic solutions of a certain differential equation// Trans. Am. Math. Soc. - 1950. - 68. - С. 304-329.
  9. Yurko V. A. On higher-order differential operators with a singular point// Inverse Problems. - 1993. - 9, № 4. - С. 495-502.
  10. Yurko V. A. Inverse spectral problems for differential operators and their applications. - Amsterdam: Gordon and Breach Sci. Publ., 2000.
  11. Yurko V. A. Higher-order differential equations having a singularity in an interior point// Results Math. - 2002. - 42, № 1-2. - С. 177-191.
  12. Yurko V. A. Integral transforms connected with higher-order differential operators with a singularity// Integral Transforms Spec. Funct. - 2002. - 13, № 6. - С. 497-511.

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