Linear Operators: Spectral theory |
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Page 1272
... indices are different from zero . A maximal symmetric operator is one which has no proper symmetric extensions ; hence , a closed symmetric operator is maximal if at least one of its deficiency indices is zero . If both are zero , then ...
... indices are different from zero . A maximal symmetric operator is one which has no proper symmetric extensions ; hence , a closed symmetric operator is maximal if at least one of its deficiency indices is zero . If both are zero , then ...
Page 1454
... indices of T are equal . PROOF . To prove ( a ) , note that if T is bounded below , there exists a constant K such that ( Tx , x ) ≥ K ( x , x ) , x Є D ( T ) . The proof of Theorem 5 now shows that σ ( T ) is a subset of the half ...
... indices of T are equal . PROOF . To prove ( a ) , note that if T is bounded below , there exists a constant K such that ( Tx , x ) ≥ K ( x , x ) , x Є D ( T ) . The proof of Theorem 5 now shows that σ ( T ) is a subset of the half ...
Page 1612
... indices of 7 are ( n , n ) . ( 8 ) If the functions ( 1 / p , ) ' , Pn - 1 , Po are integrable , if • • • , lim p1 ( t ) > 0 ∞ + 7 and if q is a function of bounded variation , then the deficiency indices of t + q are ( n , n ) . ( 9 ) ...
... indices of 7 are ( n , n ) . ( 8 ) If the functions ( 1 / p , ) ' , Pn - 1 , Po are integrable , if • • • , lim p1 ( t ) > 0 ∞ + 7 and if q is a function of bounded variation , then the deficiency indices of t + q are ( n , n ) . ( 9 ) ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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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 complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions 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 kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero