Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1126
... denote by the letter U 。. Let S be a bounded operator in L2 ( C ) which commutes with each projection U1EU . Let 1 denote the function in L2 ( C ) which is identically equal to 1. If U1SU ( 1 ) = h ( x ) , then it is evident that ...
... denote by the letter U 。. Let S be a bounded operator in L2 ( C ) which commutes with each projection U1EU . Let 1 denote the function in L2 ( C ) which is identically equal to 1. If U1SU ( 1 ) = h ( x ) , then it is evident that ...
Page 1486
... denote the unit shift operator , so that ( Sf ) ( t ) = f ( t − 1 ) . Then , since the coefficients of t are ... denote n - dimensional unitary space . With each complex number 2 , associate a linear transformation B ( 2 ) in E " , as ...
... denote the unit shift operator , so that ( Sf ) ( t ) = f ( t − 1 ) . Then , since the coefficients of t are ... denote n - dimensional unitary space . With each complex number 2 , associate a linear transformation B ( 2 ) in E " , as ...
Page 1636
... denote a variable point in En + 1 , x will generally denote a variable point in E " , generally equal to [ y1 , ... , yn ] , and s = +1 will denote a real variable generally equal to the " distinguished " last coordinate of y . As is ...
... denote a variable point in En + 1 , x will generally denote a variable point in E " , generally equal to [ y1 , ... , yn ] , and s = +1 will denote a real variable generally equal to the " distinguished " last coordinate of y . As is ...
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