Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1099
... consider the case in which the Hilbert space is finite - dimensional . The argument in this special case is as follows . Since both sides . of ( 1 ) are continuous in T and since every finite matrix may be ap- proximated arbitrarily ...
... consider the case in which the Hilbert space is finite - dimensional . The argument in this special case is as follows . Since both sides . of ( 1 ) are continuous in T and since every finite matrix may be ap- proximated arbitrarily ...
Page 1305
... considering some simple examples of differential operators . The simplest example of a formally self adjoint differential operator is the operator = 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 = i ( d / dt ) . We shall consider three choices for the interval I. ▾ Case 1 : I [ 0 ...
Page 1384
... consider expansions in the complete orthonormal set of Fourier functions 1 1 1 1 1 , sin 2лx , cos 2лx , sin 4лx , cos 4лx , etc. √2 √2 V2 √2 Let us now consider a number of singular examples . Suppose , for instance , that we study ...
... consider expansions in the complete orthonormal set of Fourier functions 1 1 1 1 1 , sin 2лx , cos 2лx , sin 4лx , cos 4лx , etc. √2 √2 V2 √2 Let us now consider a number of singular examples . Suppose , for instance , that we study ...
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