Linear Operators: Spectral theory |
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Page 1662
... subset of the interior of C , and let F be in D ( I ) . Suppose that F has a carrier Cp which is a compact subset of I. Then there is a unique distribution G in D ( C ) such that F = GI and Co - CF. In later sections , the distribution ...
... subset of the interior of C , and let F be in D ( I ) . Suppose that F has a carrier Cp which is a compact subset of I. Then there is a unique distribution G in D ( C ) such that F = GI and Co - CF. In later sections , the distribution ...
Page 1663
... subset I。 of I whose closure is compact and contained in I will be denoted by A ( I ) . m 36 DEFINITION . Let I be an open subset of C. Let k be an integer , positive or negative . Let { I } , m ≥ 1 , be a sequence of open subsets of ...
... subset I。 of I whose closure is compact and contained in I will be denoted by A ( I ) . m 36 DEFINITION . Let I be an open subset of C. Let k be an integer , positive or negative . Let { I } , m ≥ 1 , be a sequence of open subsets of ...
Page 1696
... subset Cm of I , and such that Fm → F as m → ∞ . Hence , we can evidently suppose without loss of generality that the carrier C of F is a compact subset of I. If I is included in a cube D , it follows from Lemmas 13 , 3.43 and 3.12 ...
... subset Cm of I , and such that Fm → F as m → ∞ . Hence , we can evidently suppose without loss of generality that the carrier C of F is a compact subset of I. If I is included in a cube D , it follows from Lemmas 13 , 3.43 and 3.12 ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers 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 Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero