Results 221 to 230 of about 22,371 (264)

Volterra Integral and Functional Equations

1990
The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology. This text shows that the theory of Volterra equations exhibits a rich variety of features not present in the theory of ordinary differential equations.
G. Gripenberg, S. O. Londen, O. Staffans
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Integral and functional equations

1960
An equation for a function u (x 1, x 2, ..., x n ) of n independent variables x 1, x 2, ..., x n , in the simplest case for a function y(x), is called an integral equation when it involves an integral with the function u appearing in its integrand and with at least one of the arguments of u among its variables of integration.
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Integrable solutions of a functional-integral equation

1992
A theorem about the existence of solutions of the functional-integral equation (1) \(x(t)=f\left(t,\int^ 1_ 0k(t,s)g(s,x(s))ds\right)\), \(t\in[0,1]\), is proved. The technique used in the proof depends on an interesting conjunction of the notions of the measure of weak noncompactness and the Schauder fixed point principle. It is worth while to mention
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Functional equations for path integrals

Journal of Statistical Physics, 1984
We consider the density matrices that arise in the statistical mechanics of the electron-phonon systems. In the path integral representation the phonon coordinates can be eliminated. This leads to an action that depends on pairs of points on a path, that depends explicitly on time differences, and that contains the phonon occupation numbers.
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Functional equations for Feynman integrals

Physics of Particles and Nuclei Letters, 2011
New types of equations for Feynman integrals are found. It is shown that the latter satisfy functional equations that relate integrals with different kinematics. A regular method for obtaining such relations is proposed. A derivation of the functional equations for one-loop two-, three-, and four-point functions with arbitrary masses and external ...
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Integrable solutions of a functional equation related to Wilson's equation

Publicationes Mathematicae Debrecen, 2003
The authors study for \(a>0\) and \(b>0\) the functional equation \[ af(x)+bf(y)=f(ax+by)g(y-x),\qquad x,y\in \mathbb R, \] where the functions \(f,g:\mathbb R\to \mathbb R\) are assumed to be locally integrable and continuous at the origin, respectively. They find the solutions under various assumptions on \(f(0)\) and \(g(0)\) and the derivatives of \
Choczewski, B., Powązka, Z.
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Integral Equations for the Schrödinger Wave Function

American Journal of Physics, 1959
For many problems in quantum mechanics it proves to be useful to write the Schrödinger equation as an integral equation rather than as a differential equation. In this paper we describe how the transformation of the Schrödinger equation from differential form to integral form may be accomplished.
Tobocman, W., Foldy, L. L.
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Green’s Functions and Integral Equations

1986
In this and subsequent chapters we shall be concerned with the vibration of, and in particular the inverse problems for, three systems with continuously distributed mass: the taut vibrating string, and the rod in longitudinal or torsional vibration. In the first three sections of this chapter we shall state the governing differential equations, discuss
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Using Functional Equations to Calculate Feynman Integrals

Theoretical and Mathematical Physics, 2019
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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FUNCTIONAL INTEGRALS CONNECTED WITH OPERATOR EVOLUTION EQUATIONS

Russian Mathematical Surveys, 1962
CONTENTSIntroduction § 1. The discrete case § 2. Quasi-measures and functional integrals § 3. Basic and generalized elements of Hilbert space § 4. Evolution equations § 5. Abstract hyperbolic equations § 6. Fundamental solutions of evolution equations § 7. Functional integrals associated with abstract parabolic equations § 8.
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