FEAT 发表于 2025-3-23 12:08:01

http://reply.papertrans.cn/20/1901/190065/190065_11.png

Palpate 发表于 2025-3-23 16:52:11

http://reply.papertrans.cn/20/1901/190065/190065_12.png

Cerumen 发表于 2025-3-23 21:38:15

http://reply.papertrans.cn/20/1901/190065/190065_13.png

Essential 发表于 2025-3-24 01:23:47

http://reply.papertrans.cn/20/1901/190065/190065_14.png

reception 发表于 2025-3-24 03:24:21

Measure Spaces,A matrix is a function. A complex . × . (rectangular) matrix, for example, is a function . from the Cartesian product {1,...,.} × {1,...,.} to the set ℂ 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 .(., .).

Kinetic 发表于 2025-3-24 09:25:17

Domains,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.

LEVER 发表于 2025-3-24 14:01:13

Examples,The 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.

轻弹 发表于 2025-3-24 17:53:32

http://reply.papertrans.cn/20/1901/190065/190065_18.png

reception 发表于 2025-3-24 20:52:06

Carleman Kernels,There is a sense in which the most natural integral operators on .. are the ones induced by Carleman kernels (the semi-square-integrable kernels ., for which .(.,·)∈ ..(.) for almost every .).

惹人反感 发表于 2025-3-25 00:56:55

http://reply.papertrans.cn/20/1901/190065/190065_20.png
页: 1 [2] 3 4 5 6
查看完整版本: Titlebook: Bounded Integral Operators on L 2 Spaces; Paul Richard Halmos,Viakalathur Shankar Sunder Book 1978 Springer-Verlag Berlin Heidelberg 1978