Theory of Functionals and of Integral and Integro-Differential Equations

By V. Volterra. 2005

1,256 citations recorded by the source corpus.

Subfields: Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/141e97a1cdf859b7c66be8dd047c93de33f349a0

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Citations in the corpus

Model-free control (2013, methodology): “We are employing • rather old-fashioned functional analysis, which goes back to Volterra (1910, 1930); Volterra & P´er`es (1936).”
Echo state networks are universal (2018, methodology): “A first solution to this problem in the dynamic context was pioneered in the works of Fréchet [Frec 10] and Volterra [Volt 30] one century ago when they proved that finite Volterra series can be 1Department of Mathematics and Statistics.”
Reduction of the Hodgkin-Huxley Equations to a Single-Variable Threshold Model (1997, methodology): “In this appendix we treat Volterra’s theory (Volterra, 1959) in the context of inhomogeneous differential equations, indicate under what conditions and how the kernels of the Volterra series can be computed analytically, and isolate the mathematical essentials of our own approach.”
Advanced Techniques in RF Power Amplifier Design (2002, methodology): “Successful implementations of EER which demonstrate some alleviation to these problems have appeared in recent literature [2].”
Elasticity for economic processes with memory: Fractional differential calculus approach (2016, background): “An important property of processes with memory is a decay property of memory, a “fading of memory” [31, 32, 33].”
SPIKING NEURON MODELS Single Neurons , Populations , Plasticity (2002, background): “19) about the resting state u i = u pre j = urest in a Volterra series (Volterra, 1959; Palm and Poggio, 1977; van Hemmen et al., 2000).”
Spike-triggered neural characterization. (2006, methodology): “…has been employed to estimate 93 the terms of a Wiener/Volterra expansion (Korenberg, 94 Sakai, & Naka, 1989; Marmarelis & Marmarelis, 1978; 95 Volterra, 1959; Wiener, 1958), in which the mapping from 96 stimuli to firing rate is described using a low-order 97 polynomial (see Dayan & Abbott,…”
A phenomenological theory of damping in ferromagnetic materials (2004, background): “4A functional F [f(x)] differs from a function f(x) in that a particular value of a function f(x) depends on a particular value of the numerically valued independent variable x, whereas a particular value of a functional F [f(x)] depends on the entire set values of the function f(x), [19].”