Volterra operator information

of functional analysis and operator theory, the Volterra operator, named after Vito Volterra, is a bounded linear operator on the space L2[0,1] of complex-valued...

_{a}^{t}K(t,s)x(s)\,ds.} In operator theory, and in Fredholm theory, the corresponding operators are called Volterra operators. A useful method to solve...

expressed in operator form which motivates the definition of the following operator called the nonlinear Volterra-Hammerstein operator: ( H y ) ( t )...

series Product integral Volterra operator Volterra space Volterra Semiconductor Poincaré lemma Whittaker, E. T. (1941). "Vito Volterra. 1860-1940". Obituary...

&{\mbox{otherwise}}.\end{matrix}}\right.} The Volterra operator is the corresponding integral operator T on the Hilbert space L2(0,1) given by T f ( x...

itself, Volterra series, came into use a few years later. The theory of the Volterra series can be viewed from two different perspectives: An operator mapping...

The Volterra equation may refer to the Volterra integral equation, an integral in the style of Fredholm theory. Product integral, an integral over an...

compact operator on a Hilbert space that is not self-adjoint is the Volterra operator, defined for a function f ∈ L 2 ( [ 0 , 1 ] ) {\displaystyle f\in...

V(t_{1})U(t_{1},t_{0})},} which is ultimately a type of Volterra integral. An iterative solution of the Volterra equation above leads to the following Neumann series:...

below) has constants as integration limits. A closely related form is the Volterra integral equation which has variable integral limits. An inhomogeneous...

ordered exponential is used in matrix and operator algebras. It is a kind of product integral, or Volterra integral. Let A be an algebra over a field...

case of composition products considered by the Italian mathematician Vito Volterra in 1913. When a function gT is periodic, with period T, then for functions...

quasinilpotent element is a topological divisor of zero (e.g. the Volterra operator). An operator on a Banach space X {\displaystyle X} , which is injective...

expression of the kernel of an operator. All these models can be represented by a Volterra series but in this case the Volterra kernels take on a special form...

technique for computing the Volterra integral. Examples include the Dyson expansion, the integrals that occur in the operator product expansion and the...

been introduced in 1887 by the Italian mathematician and physicist Vito Volterra. The theory of nonlinear functionals was continued by students of Hadamard...

g\;:\;(t,u)\mapsto \int _{0}^{t}G(t,\tau )u(\tau )\,d\tau } is a Volterra operator. In this more general formulation the embedding procedure of Lindquist...

(1993), the connections between the theory of spatial martingales and Volterra operators with goodness of fit problems of statistics was demonstrated, and...

with non-commutative vector fields and represent their flows as infinite Volterra series. These series, at first introduced as purely formal expansions,...

use in general has been attributed to mathematician and physicist Vito Volterra and its founding is largely attributed to mathematician Stefan Banach....

The explicit term on the right-hand side is the leading order term of a Volterra expansion for the full nonlinear response. If the system in question is...

Imbert-Vier, Simon (2018-10-08), Shiferaw Bekele; Uoldelul Chelati Dirar; Volterra, Alessandro; Zaccaria, Massimo (eds.), "Living the War Far Away from the...

Menger sponge Mosely snowflake Sierpiński carpet Sierpiński triangle Smith–Volterra–Cantor set, also called the fat Cantor set − A closed nowhere dense (and...

particular, of oscillatory systems such as predator-prey models (see Lotka–Volterra equations). In these models the phase paths can "spiral in" towards zero...

gravitational motion Integrable lattice models Ablowitz–Ladik lattice Toda lattice Volterra lattice Integrable systems in 1 + 1 dimensions AKNS system Benjamin–Ono...

equation (also known as Fisher's equation) to model population growth Lotka–Volterra equations to describe the dynamics of biological systems in which two species...