解脱
发表于 2025-3-23 12:54:57
https://doi.org/10.1007/978-3-663-13498-5We begin by applying Theorem 3.42 and Corollary 3.44 to the Fredholm theory of Toeplitz operators. Although this chapter is concerned with Toeplitz operators on H. ≅ 1., we first state some results for Toeplitz operators on H. and 1., because there do not arise any substantial difficulties when passing from the case . = 2 to the case . ≠ 2.
poliosis
发表于 2025-3-23 17:53:19
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使习惯于
发表于 2025-3-23 20:52:08
Leistungszusage bei Unsicherheit,Let 1 ≤ . < ∞ and let . be a subset of ℤ. (. = 1, 2, ...).
hematuria
发表于 2025-3-24 00:02:59
Leistungszusage bei Sicherheit,Throughout this chapter we let L. and L. (1≤P≤∞) refer to the L. spaces of Lebesgue measure on ℝ and ℝ., respectively. The L. spaces on the unit circle will be denoted by L.(T). The operator . defined by.:L.→L.., . ↦ . | ℝ.is clearly bounded for 1 ≤ . ≤ ∞.
chastise
发表于 2025-3-24 04:08:11
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anticipate
发表于 2025-3-24 09:42:50
Basic theory,If a ∈ L∞ and 1 <p< ∞ ,then the operator.is obviously bounded and .It is called the . L. generated by the function a. For f ∈ L. and .∈ L.(1/.+1/.=1), write .It is clear that is equal to the th Fourier coefficient of a. The following proposition shows that every bounded operator with such a property is a multiplication operator.
愤慨一下
发表于 2025-3-24 11:15:12
Symbol analysis,Let . be a closed subset of . = .(L.) and let . ∈ L.. The matrix function . is called . if there exist a real number . > 0 and two invertible matrices ., . ∈ ℂ. such that Re (.(.) .) ≧ . for all . ∈ ., that is,.and . is said to be . if.that is, if each matrix in the closed convex hull of .(.) is invertible.
miscreant
发表于 2025-3-24 18:19:45
Toeplitz operators on H2,We begin by applying Theorem 3.42 and Corollary 3.44 to the Fredholm theory of Toeplitz operators. Although this chapter is concerned with Toeplitz operators on H. ≅ 1., we first state some results for Toeplitz operators on H. and 1., because there do not arise any substantial difficulties when passing from the case . = 2 to the case . ≠ 2.
Badger
发表于 2025-3-24 19:17:47
Toeplitz operators on l,,We have already settled the Fredholm theory of the operators in alg (Corollaries 4.7 and 4.8) and stated a localization result for Toeplitz operators on l. (Theorem 2.95). This chapter is devoted to some more delicate questions of the l.. theory of Toeplitz operators.
Ingest
发表于 2025-3-25 00:29:15
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