Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1224
... symmetric extension of a symmetric operator T with dense domain , we have only to restrict T * to some suitably chosen subdomain of D ( T * ) . Keeping this basic principle firmly in mind , we embark upon a systematic study of the ...
... symmetric extension of a symmetric operator T with dense domain , we have only to restrict T * to some suitably chosen subdomain of D ( T * ) . Keeping this basic principle firmly in mind , we embark upon a systematic study of the ...
Page 1236
... symmetric extension of T is the restriction of T * to the subspace of D ( T * ) determined by a symmetric family of boundary conditions , B ( x ) = 0 , i = 1 , ... , k . Conversely , every such restriction T1 of T * is a closed ...
... symmetric extension of T is the restriction of T * to the subspace of D ( T * ) determined by a symmetric family of boundary conditions , B ( x ) = 0 , i = 1 , ... , k . Conversely , every such restriction T1 of T * is a closed ...
Page 1272
... symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has no proper ...
... symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has no proper ...
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