Integral operator - Wikipedia
An integral operator is an operator that involves integration. Special instances are: The operator of integration itself, denoted by the integral symbol; Integral linear operators, which are linear operators induced by bilinear forms involving integrals; Integral transforms, which are maps between two function spaces, which involve integrals
希尔伯特-施密特算子 - 维基百科，自由的百科全书
在数学中，一个希尔伯特-施密特算子(英語： Hilbert–Schmidt operator)（得名于大卫·希尔伯特和埃哈德·施密特）, 是希尔伯特空间H上的有界算子 A，有有限的希尔伯特-施密特范数
Integral operator - Encyclopedia of Mathematics
2024年7月5日 · A mapping $ x \mapsto A x $ in which the law of the correspondence $ A $ is given by an integral. An integral operator is sometimes called an integral transformation.
For the moment we can work with a general function u 2 L2(0; 2 ) { or think of it as continuous if you prefer. The truncated Fourier series of u is a nite linear combination of the ek : where I have just inserted the de nition of the ck's into the sum.
Hilbert–Schmidt integral operator - Wikipedia
In mathematics, a Hilbert–Schmidt integral operator is a type of integral transform. Specifically, given a domain Ω in n - dimensional Euclidean space Rn, then the square-integrable function k : Ω × Ω → C belonging to L2(Ω×Ω) such that. is called a Hilbert–Schmidt kernel and the associated integral operator T : L2(Ω) → L2(Ω) given by.
对称核线性积分算子 - 百度百科
对称核线性积分算子(linear integral operator with symmetric kernel)是具有对称核的线性积分算子，又称为具有埃尔米特核的线性积分算子。 对称核线性积分算子理论，是有限维空间对称矩阵理论在无穷维空间的推广。
We consider linear integral operators K of the form (1.1) Ku(y) = Z k(x,y)u(x)dµ(x), where the kernel k is a complex-valued measurable function with respect to the σ-algebra Σµ⊗ν. We seek conditions on k that imply the operator K is bounded or even compact from X to
Hilbert-Schmidt integral operator - Encyclopedia of Mathematics
2020年6月5日 · A Hilbert–Schmidt integral operator is a self-adjoint operator if and only if $ K ( x, y) = \overline{ {K ( y, x) }}\; $ for almost-all $ ( x, y) \in X \times X $( with respect to $ ( \mu \times \mu ) $). For a self-adjoint Hilbert–Schmidt integral operator and for its kernel the following expansions are valid:
2020年10月3日 · If k ∈ L2(R2), then the integral operator Lk given by equa- tion (8.1) defines a bounded mapping of L 2 (R) into itself, and its operator norm satisfies kL k k ≤ kkk 2 .
Integral Operators - SpringerLink
2023年3月14日 · Compared to conventional integrals, integral operators make formulas clearer and calculations easier to perform. These advantages of integral operators shall be demonstrated by a typical example. A function f is integrated over a path leading from a point in the glacier in z- direction to its free surface.
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