Linear Operators: Spectral operators |
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Page 1998
... examples are among the most familiar convolutions in 2 . EXAMPLE ( Translation ) . Let λ ( o ) = 1 if t is in o ; otherwise let λ ( o ) = 0 . Then ( λ , * q ) ( s ) = q ( st ) . Then 12 EXAMPLE ( Convolution by an L1 function ) . Let ƒ ...
... examples are among the most familiar convolutions in 2 . EXAMPLE ( Translation ) . Let λ ( o ) = 1 if t is in o ; otherwise let λ ( o ) = 0 . Then ( λ , * q ) ( s ) = q ( st ) . Then 12 EXAMPLE ( Convolution by an L1 function ) . Let ƒ ...
Page 1999
... example shows that where Ф is in L1 is in L2 and thus ƒ * q = q * f = [ _ÿ ( 8 ) e ( ds ) f 7 ( ƒ * q ) = [ _õ ( s ) ... EXAMPLE ( Principal value convolutions ) . A point so in S is called a singular point for the measurable function ƒ ...
... example shows that where Ф is in L1 is in L2 and thus ƒ * q = q * f = [ _ÿ ( 8 ) e ( ds ) f 7 ( ƒ * q ) = [ _õ ( s ) ... EXAMPLE ( Principal value convolutions ) . A point so in S is called a singular point for the measurable function ƒ ...
Page 2020
... example , with p = 2 , is the perturbed Laplacian ( 19 ) A = ( 2 22 22 a 2 - + ... + Əs2 and a = Here a ( Ələs1 ... example which has features not seen in the preceding examples is given by the formal differential operator ( 21 ) a 081 A ...
... example , with p = 2 , is the perturbed Laplacian ( 19 ) A = ( 2 22 22 a 2 - + ... + Əs2 and a = Here a ( Ələs1 ... example which has features not seen in the preceding examples is given by the formal differential operator ( 21 ) a 081 A ...
Contents
SPECTRAL OPERATORS | 1924 |
14 | 1983 |
Sufficient Conditions | 2134 |
Copyright | |
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A₁ adjoint operator algebra of projections Amer analytic arbitrary asymptotic B₁ Banach space Boolean algebra Borel set boundary conditions bounded Borel function bounded linear operator bounded operator commuting compact complete Boolean algebra complex numbers complex plane continuous functions converges Corollary countably additive Definition denote differential operator Doklady Akad domain E₁ eigenvalues elements equation exists finite number follows from Lemma follows from Theorem follows immediately formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality inverse L₁ Lebesgue Math multiplicity Nauk SSSR norm operators in Hilbert perturbation PROOF properties prove quasi-nilpotent resolution Russian satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset Suppose trace class type spectral operator unbounded uniformly bounded vector zero