动物
发表于 2025-3-27 00:29:29
Ferd Williams,B. Baron,S. P. Varmane that asks which operators . be integral operators (§16). The problem is one of recognition: if an integral operator on ..(.) is described in some manner other than by its kernel, how do its operatorial and measure-theoretic properties reflect the existence of a kernel that induces it? (Cf. Proble
Meager
发表于 2025-3-27 04:19:53
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Minatory
发表于 2025-3-27 07:21:05
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cutlery
发表于 2025-3-27 13:14:20
Uniqueness, to ..(.). It is natural to ask: is that linear transformation injective? In other words: is an integral operator induced by only one kernel? The content of the following assertion is that the answer is yes.
PRE
发表于 2025-3-27 15:42:43
Essential Spectrum,ty operator on ..(ℝ.) (which is not an integral operator) and the tensor product of the identity operator on ..(ℤ.) with a projection of rank 1 on ..(II) (which is an integral operator). What is the essential difference between these two kinds of examples?
diskitis
发表于 2025-3-27 19:34:59
Characterization,ators? The question refers to unitary equivalence; in precise terms, it asks for a characterization of those operators . on ..(.) for which there exists a unitary operator . on ..(.) such that .* is integral.
表脸
发表于 2025-3-28 01:37:48
Universality,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 ..(.).
舔食
发表于 2025-3-28 06:03:10
Book 1978an 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
警告
发表于 2025-3-28 07:58:38
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analogous
发表于 2025-3-28 13:30:05
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