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Titlebook: Bounded Integral Operators on L 2 Spaces; Paul Richard Halmos,Viakalathur Shankar Sunder Book 1978 Springer-Verlag Berlin Heidelberg 1978

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樓主
發(fā)表于 2025-3-21 17:49:34 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
期刊全稱Bounded Integral Operators on L 2 Spaces
影響因子2023Paul Richard Halmos,Viakalathur Shankar Sunder
視頻videohttp://file.papertrans.cn/191/190065/190065.mp4
學(xué)科分類Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge
圖書封面Titlebook: Bounded Integral Operators on L 2 Spaces;  Paul Richard Halmos,Viakalathur Shankar Sunder Book 1978 Springer-Verlag Berlin Heidelberg 1978
影響因子The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ‘ spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali- zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea- sure spaces. The category. Some of the flavor of the theory can be perceived in
Pindex Book 1978
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沙發(fā)
發(fā)表于 2025-3-21 20:38:36 | 只看該作者
978-3-642-67018-3Springer-Verlag Berlin Heidelberg 1978
板凳
發(fā)表于 2025-3-22 04:10:59 | 只看該作者
Luminescence-Based Authenticity Testing,ake use of the infinite amount of room in ?., i.e., of the infinite measure. The answer is yes for II also, and the proof is not difficult, but it is better understood and more useful if instead of being attacked head on, it is embedded into a larger context.
地板
發(fā)表于 2025-3-22 05:06:18 | 只看該作者
5#
發(fā)表于 2025-3-22 10:13:54 | 只看該作者
Luminescence in Electrochemistryty operator on ..(?.) (which is not an integral operator) and the tensor product of the identity operator on ..(?.) with a projection of rank 1 on ..(II) (which is an integral operator). What is the essential difference between these two kinds of examples?
6#
發(fā)表于 2025-3-22 13:46:51 | 只看該作者
7#
發(fā)表于 2025-3-22 19:20:21 | 只看該作者
Apparatus for Bioluminescence Measurements,ad of the existential one. In precise terms: under what conditions on an operator . on ..(.) does it happen that .* is an integral operator for every unitary . on ..(.)? When it does happen, the operator . will be called a . integral operator on ..(.).
8#
發(fā)表于 2025-3-23 01:07:43 | 只看該作者
https://doi.org/10.1007/978-3-030-67311-6A matrix is a function. A complex . × . (rectangular) matrix, for example, is a function . from the Cartesian product {1,...,.} × {1,...,.} to the set ? of complex numbers; its value at the ordered pair <., .> is usually denoted by ... In this book it will always be denoted by the typographically and conceptually more convenient symbol .(., .).
9#
發(fā)表于 2025-3-23 05:24:26 | 只看該作者
Enantioselective Sensing by Luminescence,The way a matrix acts is defined by the familiar formula . The generalization to arbitrary kernels is formally obvious: . Finite sums such as the ones in (1) can always be formed; integrals such as theones indicated in (2) may fail to exist and, even when they exist, may fail todefine well-behaved functions.
10#
發(fā)表于 2025-3-23 08:13:03 | 只看該作者
Luminescence Centers in CrystalsThe easiest examples of bounded kernels are the square-integrable ones introduced in Lemma 4.1; they induce Hilbert-Schmidt operators. The examples that follow are different; they are, for one thing, not compact.
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