Linear Operators, Part 2 |
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Page 1044
... consider the function hε ( z ) = exp ( -Ez - 2-8 ) g ( z ) . Since | arg ( 2-2- ) | < ( 2 + 8 ) ( π / 4 − d ) ≤ л / 2 — § , for all z in σ1 , we have | exp ( -2-2-8 ) ≤ 1 , Ζε σι [ + ] and even ZE 01 . [ ++ ] | exp ( −ɛz − 2−8 ) ...
... consider the function hε ( z ) = exp ( -Ez - 2-8 ) g ( z ) . Since | arg ( 2-2- ) | < ( 2 + 8 ) ( π / 4 − d ) ≤ л / 2 — § , for all z in σ1 , we have | exp ( -2-2-8 ) ≤ 1 , Ζε σι [ + ] and even ZE 01 . [ ++ ] | exp ( −ɛz − 2−8 ) ...
Page 1155
... consider the special form that the results of Sections 3 and 4 take when R is a compact Abelian group , a case studied ex- plicitly in Section 1 . 8 THEOREM . If R is a compact Abelian group , its character group R is discrete ...
... consider the special form that the results of Sections 3 and 4 take when R is a compact Abelian group , a case studied ex- plicitly in Section 1 . 8 THEOREM . If R is a compact Abelian group , its character group R is discrete ...
Page 1305
... considering some simple examples of differential operators . The simplest example of a formally self adjoint differential operator is the operator τ = i ( d / dt ) . We shall consider three choices for the interval I. Case 1 : I = [ 0 ...
... considering some simple examples of differential operators . The simplest example of a formally self adjoint differential operator is the operator τ = i ( d / dt ) . We shall consider three choices for the interval I. Case 1 : I = [ 0 ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero