Results 151 to 160 of about 540,702 (189)

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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Function Spaces and Integral Equations

1986
The set E ⊂ R n is called a set of (n-dimensional) measure zero if for each positive e there exists a countable set of open (n-dimensional) cubes that cover E and whose total volume is less than e.
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Extended Dissipativity Analysis for Markovian Jump Neural Networks via Double-Integral-Based Delay-Product-Type Lyapunov Functional

IEEE Transactions on Neural Networks and Learning Systems, 2021
Yufeng Tian, Zhanshan Wang
exaly  

The mechanisms of integral membrane protein biogenesis

Nature Reviews Molecular Cell Biology, 2021
Ramanujan Shankar Hegde, Robert J Keenan
exaly  

Analytic functions Integral transforms Differential equations

2015
TOMARELLI, FRANCO, GAZZOLA, FILIPPO, Maurizio Zanotti   +2 more
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INTEGRAL EQUATIONS FOR HEUN FUNCTIONS

The Quarterly Journal of Mathematics, 1942
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