Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 CG = CF. In later sections , the ...
... 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 CG = CF. In later sections , the ...
Page 1663
... subset I。 of I whose closure is compact and contained in I will be denoted by A - * ) ( I ) . 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 ...
... subset I。 of I whose closure is compact and contained in I will be denoted by A - * ) ( I ) . 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 ...
Page 1696
... subset Cm of I , and such that F. → F as moo . 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 that ...
... subset Cm of I , and such that F. → F as moo . 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 that ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum 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(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero