Results 171 to 180 of about 14,741 (209)

Symbolic Computation with Integro-Differential Operators

Proceedings of the ACM on International Symposium on Symbolic and Algebraic Computation, 2016
The algebraic and algorithmic study of integro-differential algebras and operators has only started in the past decade. Integro-differential operators allow us in particular to study initial value and boundary problems for linear ODEs from an algebraic point of view.
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On Singular Integro‐Differential Operators on the Halfaxis

Mathematische Nachrichten, 1987
AbstractIn the frame of classical SOBOLEV spaces the FREDHOLM property will be characterized for a class of singular integro‐differential operators on the positive halfaxis. A symbol calculus moreover permits to specify an index formula and a special FREDHOLM inverse.
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Inverse problems for first-order integro-differential operators

Mathematical Notes, 2016
The author is concerned with the problem of reconstructing the continuous functions \(M(x,t)\), and \(R(x)\), \(V(x)\), \(0\leq t\leq x\leq \pi\) from the integrodifferential equations: \[ iy'(x) + \int^{x}_{0} M(x,t) y(t) dt = \lambda y(x),\quad x\in [0,\pi], \quad\text{ and} \] \[ iy'(x) + \int^{x}_{0} M(x,t) y(t)dt + R(x) \int^{\pi}_{0} V(t) y(t) dt
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Inverse spectral problem for integro-differential operators

Mathematical Notes, 2007
In 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 Mathematics
zbMATH 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, 1956
the 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, 2004
The 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

1984
Publisher 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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Integrative oncology: Addressing the global challenges of cancer prevention and treatment

Ca-A Cancer Journal for Clinicians, 2022
Jun J Mao,, Msce, Lorenzo Cohen, Karen M Mustian   +2 more
exaly  

An Integro-Differential Operator

Journal of the London Mathematical Society, 1973
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