Linear Operators, Part 2 |
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Page 1272
... deficiency 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 ...
... deficiency 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 ...
Page 1400
... deficiency indices of τ are both equal to an integer k and ( a ) for every self adjoint extension T of To ( T ) , the dimension of the null - space { f \ Tf = λf } is at most k ; ( b ) there exist self adjoint extensions T of To ( t ) ...
... deficiency indices of τ are both equal to an integer k and ( a ) for every self adjoint extension T of To ( T ) , the dimension of the null - space { f \ Tf = λf } is at most k ; ( b ) there exist self adjoint extensions T of To ( t ) ...
Page 1612
... deficiency indices of 7 are ( n , n ) . ( 8 ) If the functions ( 1 / p ) ' , Pn - 1 , ... , Po are integrable , if lim p , ( t ) > 0 ∞17 and if q is a function of bounded variation , then the deficiency indices of t + q are ( n , n ) ...
... deficiency indices of 7 are ( n , n ) . ( 8 ) If the functions ( 1 / p ) ' , Pn - 1 , ... , Po are integrable , if lim p , ( t ) > 0 ∞17 and if q is a function of bounded variation , then the deficiency indices of t + q are ( n , n ) ...
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 domain 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 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 open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma 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