In mathematics, a Hilbert–Schmidt operator, named after David Hilbert and Erhard Schmidt, is a bounded operator A : H → H {\displaystyle A\colon H\to...

In mathematics, a Hilbert–Schmidt integral operator is a type of integral transform. Specifically, given a domain Ω in Rn, any k : Ω × Ω → C such that...

In mathematics, Hilbert–Schmidt may refer to a Hilbert–Schmidt operator; a Hilbert–Schmidt integral operator; the Hilbert–Schmidt theorem. This disambiguation...

class of operators known as Hilbert–Schmidt operators that are especially important in the study of integral equations. Fredholm operators differ from...

Hilbert operator may refer to: The epsilon operator in Hilbert's epsilon calculus The Hilbert–Schmidt operators on a Hilbert space Hilbert–Schmidt integral...

bounded operator T : H 1 ⊗ H 2 → K {\displaystyle T:H_{1}\otimes H_{2}\to K} such that L = T p . {\displaystyle L=Tp.} A weakly Hilbert-Schmidt mapping...

It states that a bounded linear operator between two Hilbert spaces is γ-radonifying if it is a Hilbert–Schmidt operator. The result is also important in...

operator on Hilbert space is an extension of the concept of a matrix acting on a finite-dimensional vector space; in Hilbert space, compact operators...

integral operator. T is equal to the composition of two Hilbert-Schmidt operators. | T | {\textstyle {\sqrt {|T|}}} is a Hilbert-Schmidt operator. Let T...

L ( H ) {\displaystyle L(H)} are the trace-class, Hilbert–Schmidt operators, and compact operators. F ( H ) {\displaystyle F(H)} is dense in all three...

arithmetic of ends Hilbert's paradox of the Grand Hotel Hilbert–Schmidt operator Hilbert–Smith conjecture Hilbert–Burch theorem Hilbert's irreducibility theorem...

twentieth century. Schmidt was born in Tartu (German: Dorpat), in the Governorate of Livonia (now Estonia). His advisor was David Hilbert and he was awarded...

the Hilbert–Schmidt theorem, also known as the eigenfunction expansion theorem, is a fundamental result concerning compact, self-adjoint operators on Hilbert...

analysis and harmonic analysis. The two main singular integral operators, the Hilbert transform and the Cauchy transform, can be defined for any smooth...

is a Hilbert–Schmidt operator, hence in particular is compact. V has no eigenvalues and therefore, by the spectral theory of compact operators, its spectrum...

the trace class norm and the Hilbert–Schmidt norm. Let H 1 {\displaystyle H_{1}} , H 2 {\displaystyle H_{2}} be Hilbert spaces, and T {\displaystyle T}...

}^{-1/2}C_{\nu }^{1/2})(C_{\mu }^{-1/2}C_{\nu }^{1/2})^{\ast }-I} is a Hilbert–Schmidt operator on H ¯ . {\displaystyle {\bar {H}}.} A simple consequence of the...

pairs of points. Associated to K is a linear operator (more specifically a Hilbert–Schmidt integral operator when the interval is compact) on functions...

functional analysis, a normal operator on a complex Hilbert space H {\displaystyle H} is a continuous linear operator N : H → H {\displaystyle N\colon...

mathematics, a symmetrizable compact operator is a compact operator on a Hilbert space that can be composed with a positive operator with trivial kernel to produce...

Schatten-class operator is a bounded linear operator on a Hilbert space with finite pth Schatten norm. The space of pth Schatten-class operators is a Banach...

strong operator topology to H. Moreover, if Vf(z) = f(H(z)), then VHV−1 − H is an operator with smooth kernel, so a Hilbert–Schmidt operator. In fact...

conjecture Hilbert–Schmidt inner product Hilbert–Schmidt norm Hilbert–Schmidt operator Hilbert–Schmidt integral operator Hilbert–Schmidt theorem Hilbert–Serre...

their counter-part in finite dimension. In Hilbert spaces such operators are usually called trace class operators and one can define such things as the trace...

operator theory due to Hermann Weyl and John von Neumann. It states that, after the addition of a compact operator (Weyl (1909)) or Hilbert–Schmidt operator...

\varphi _{2}} , ... are the orthonormal eigenfunctions of the linear Hilbert–Schmidt operator G : L 2 ( T ) → L 2 ( T ) , G ( f ) = ∫ T G ( s , t ) f ( s ) d...

{\displaystyle {\mathfrak {A}}} . The Hilbert–Schmidt operators on an infinite-dimensional Hilbert space form a Hilbert algebra with inner product (a, b)...

finite-rank operators in an infinite-dimensional setting. When Y {\displaystyle Y} is a Hilbert space, it is true that any compact operator is a limit...

Euclidean space Fundamental theorem of Hilbert spaces Gram–Schmidt process Hellinger–Toeplitz theorem Hilbert space Inner product space Legendre polynomials...

definition the Neumann–Poincaré operator TK is the operator on L2(∂Ω) given by the kernel K(z,w). It is a Hilbert–Schmidt operator since the kernel is continuous...