Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1272
... indices are d 0 , d The operator T1 is called an elementary symmetric operator . It may be proved that if T is maximal symmetric with indices d = 0 , d_ = n ( where n is any cardinal number ) , then may be broken into a direct sum of ...
... indices are d 0 , d The operator T1 is called an elementary symmetric operator . It may be proved that if T is maximal symmetric with indices d = 0 , d_ = n ( where n is any cardinal number ) , then may be broken into a direct sum of ...
Page 1400
... 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 ) such that 2 ...
... 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 ) such that 2 ...
Page 1636
... indices for E " , that is , indices whose range of variation is restricted by the condition min J ≥ 1 , max J≤n . The symbols J1 , J , J1 will similarly denote indices for En + 1 . Thus , for instance , if § is in U " , Jm is an ...
... indices for E " , that is , indices whose range of variation is restricted by the condition min J ≥ 1 , max J≤n . The symbols J1 , J , J1 will similarly denote indices for En + 1 . Thus , for instance , if § is in U " , Jm is an ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula 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 linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero