Integral Equations and Operator Theory is a journal dedicated to operator theory and its applications to engineering and other mathematical sciences. As...

Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators. The...

{\displaystyle K(t,u)=K(u,t)} . In the theory of integral equations, symmetric kernels correspond to self-adjoint operators. There are many classes of problems...

functional analysis and its applications to related fields. These include: Differential equations and Integral equations Complex analysis and Harmonic analysis...

1927) was a Swedish mathematician whose work on integral equations and operator theory foreshadowed the theory of Hilbert spaces. Fredholm was born in Stockholm...

is an integral operator acting on u. Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving...

Lorentz covariance (time and space components of quantities enter equations in the same way) is easier to achieve than in the operator formalism of canonical...

Grothendieck and Stefan Banach. The origin of the theory of compact operators is in the theory of integral equations, where integral operators supply concrete...

and Israeli mathematician, most known for his work in operator theory and functional analysis, in particular linear operators and integral equations....

partial differential equations and quantum field theory, e.g. in mathematical models that include ultrametric pseudo-differential equations in a non-Archimedean...

Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form...

theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation...

unperturbed solution, and the equations describing the system in full. Write   D   {\displaystyle \ D\ } for this collection of equations; that is, let the...

differential equations are the differential equations that are linear in the unknown function and its derivatives. Their theory is well developed, and in many...

Stochastic differential equations are in general neither differential equations nor random differential equations. Random differential equations are conjugate to...

approximate solutions of certain partial differential equations using computers. Partial differential equations also occupy a large sector of pure mathematical...

(an operator that acts on functions may act also on differential equations whose solutions are functions that satisfy the equation). (see Operator (physics)...

homogeneous equations have constant coefficients may be solved by quadrature, which means that the solutions may be expressed in terms of integrals. This is...

Fourier integral operators have become an important tool in the theory of partial differential equations. The class of Fourier integral operators contains...

mathematics, operator theory is the study of linear operators on function spaces, beginning with differential operators and integral operators. The operators may...

these equations must be solved as a Sturm–Liouville problem in terms of the eigenfunctions Xn(x) and eigenvalues λn. The second of these equations can be...

the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and the second kind...

differential equations with polynomial coefficients, and by extending the notion of Fourier transformation to include Fourier integral operators, some non-linear...

low energy limit of the Dirac theory in the following manner. First the equation is written in the form of coupled equations for 2-spinors with the SI units...

context of quantum field theory (QFT), the equations determine the dynamics of quantum fields. The solutions to the equations, universally denoted as ψ...

of linear and non-linear (partial) differential equations for generating integrable equations, to find its Lax pairs, recursion operators, Bäcklund transform...

It is the operator corresponding to the Volterra integral equations. The Volterra operator, V, may be defined for a function f ∈ L2[0,1] and a value t ∈ [0...

California, Santa Cruz, and became professor emeritus in 1994. His research areas were in integral equations and operator theory, in particular the determination...

Gottfried E. (September 1985). "Fritz Noether (1884–194?)". Integral Equations and Operator Theory. 8 (5): 573–576. doi:10.1007/BF01201702. S2CID 119721244...

In mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations. They are named in honour of Erik Ivar...