Linear Operators, Part 2 |
From inside the book
Results 1-3 of 94
Page 1998
... examples are among the most familiar convolutions in A. EXAMPLE ( Translation ) . Let ( o ) = 1 if t is in σ ; otherwise let λ ( o ) = 0 . Then ( λ ; * q ) ( s ) = q ( s − t ) . Then EXAMPLE ( Convolution by an L1 function ) . Let f be ...
... examples are among the most familiar convolutions in A. EXAMPLE ( Translation ) . Let ( o ) = 1 if t is in σ ; otherwise let λ ( o ) = 0 . Then ( λ ; * q ) ( s ) = q ( s − t ) . Then EXAMPLE ( Convolution by an L1 function ) . Let f be ...
Page 1999
... example shows that Ф is in L2 and thus * ƒ * q = q * f = [ _ÿ ( s ) e ( ds ) f = 7 ( ƒ • q ) = { ÿ ( s ) re ( ds ) ƒ = [ _5 ( 0 ) μ { dx } } = ƒ ÿ = √ } ( 8 ) μ ( ds ) ÿ which shows that f * q = = = [ _ } ( s ) e ( ds ) p . By using a ...
... example shows that Ф is in L2 and thus * ƒ * q = q * f = [ _ÿ ( s ) e ( ds ) f = 7 ( ƒ • q ) = { ÿ ( s ) re ( ds ) ƒ = [ _5 ( 0 ) μ { dx } } = ƒ ÿ = √ } ( 8 ) μ ( ds ) ÿ which shows that f * q = = = [ _ } ( s ) e ( ds ) p . By using a ...
Page 2020
... example , with p = 2 , is the perturbed Laplacian ( 19 ) V2 α A = D2 ) . .72 V2 - + + > Əs Əs and a = Here ( 20 ) a ... example which has features not seen in the preceding examples is given by the formal differential operator ( 21 ) a a ...
... example , with p = 2 , is the perturbed Laplacian ( 19 ) V2 α A = D2 ) . .72 V2 - + + > Əs Əs and a = Here ( 20 ) a ... example which has features not seen in the preceding examples is given by the formal differential operator ( 21 ) a a ...
Contents
SPECTRAL OPERATORS | 1924 |
The Canonical Reduction of a Spectral Operator | 1939 |
Bounded Spectral Operators in Hilbert Space | 1947 |
Copyright | |
26 other sections not shown
Other editions - View all
Common terms and phrases
A₁ adjoint operator algebra of projections Amer analytic arbitrary B-algebra B*-algebra B₁ Banach space Boolean algebra Borel sets boundary conditions bounded Borel function bounded linear operator bounded operator closed operator commuting compact complex numbers complex plane converges Corollary countably additive Definition denote dense differential operator Doklady Akad domain eigenvalues elements equation exists finite number follows from Lemma formal differential operator formula function f H₁ H₂ Hence Hilbert space hypothesis identity inequality integral invariant inverse L₁ Lebesgue Lemma Math multiplicity Nauk SSSR norm operators in Hilbert perturbation polynomial PROOF properties prove quasi-nilpotent resolution Russian S₁ satisfies scalar type operator scalar type spectral Section sequence shows spectral measure spectral operator spectral theory spectrum subset subspace Suppose trace class type spectral operator unbounded uniformly bounded unique vector zero