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Inverse spectral problem for integro-differential operators
Mathematical Notes, 2007In this paper, we study the inverse spectral problem on a finite interval for the integro-differential operator l which is the perturbation of the Sturm-Liouville operator by the Volterra integral operator. The potential q belongs to L2[0, π] and the kernel of the integral perturbation is integrable in its domain of definition.
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Integro-Differential Equations of Gerasimov Type with Sectorial Operators
Proceedings of the Steklov Institute of MathematicszbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fedorov, V. E., Godova, A. D.
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On an Integro-Differential Operator of the Cauchy Type
Proceedings of the American Mathematical Society, 1956the boundary conditions for (1.1) go over into boundary conditions for (1.4). An equation essentially equivalent to (1.3) was derived by Kac in [4] and treated by Kac and Pollard in [5]. Boundary conditions and construction of solutions to (1.1) were considered in [2].
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On the Theory of the Continual Integro-Differentiation Operator
Differential Equations, 2004The author considers the operator \[ D_{0x}^{[\alpha, \beta]}u(x)\equiv \int_{\alpha}^{\beta}D_{0x}^tu(x)\, dt, \tag{1} \] known as continual integro-differentiation operator, where \[ D_{0x}^t g(x)=\begin{cases} \frac{1}{\Gamma(-t)}\int_0^x g(\xi)(x-\xi)^{-t-1}\, d\xi\quad &\text{if ...
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Integro-Differential Operators and Theory of Summation
1984Publisher Summary This chapter discusses the theory of differential and integral operators of arbitrary complex order. The chapter describes some applications of the theory in modern mathematical physics, connected with the Riesz potentials. The kernel of the Riesz method is the analytic continuation of the Riemann–Liouville “fractional” integral ...
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An Integro-Differential Operator
Journal of the London Mathematical Society, 1973openaire +1 more source
Koopman operator dynamical models: Learning, analysis and control
Annual Reviews in Control, 2021Stefan Sosnowski
exaly
Nakhushev extremum principle for integro-differential operators
Итоги науки и техники Серия «Современная математика и ее приложения Тематические обзоры», 2021openaire +1 more source