Linear Operators, Part 2 |
From inside the book
Results 1-3 of 73
Page 1126
... denote by the letter U 。. 0 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 。. 0 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 | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
56 other sections not shown
Other editions - View all
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense 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 linear 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 subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero