Linear Operators: Spectral theory |
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Page 980
... complex valued homomorphism H on either A or A1 is continuous and has H ( I ) 1 it follows that H is completely determined by the values it takes on elements of the form T ( f ) with ƒ in L1 ( R ) . Thus each of the spaces M and M1 has ...
... complex valued homomorphism H on either A or A1 is continuous and has H ( I ) 1 it follows that H is completely determined by the values it takes on elements of the form T ( f ) with ƒ in L1 ( R ) . Thus each of the spaces M and M1 has ...
Page 1036
... complex valued function on the B - space of all Hilbert - Schmidt operators . ( * ) PROOF . First note that if is a complex number with || < 1 then → log e $ ( 1—5 ) = 5− ( 5 + 212 52 + 353 + - = • . ) = 0 ( 1512 ) , as 0. Let f ( 5 ) ...
... complex valued function on the B - space of all Hilbert - Schmidt operators . ( * ) PROOF . First note that if is a complex number with || < 1 then → log e $ ( 1—5 ) = 5− ( 5 + 212 52 + 353 + - = • . ) = 0 ( 1512 ) , as 0. Let f ( 5 ) ...
Page 1281
... complex - valued function integrable over every compact subinterval of I. Let to I , and let co , C1 , ... , C - 1 be an arbitrary set of n complex numbers . Then there exists a unique ƒ € A " ( I ) such that ( a ) ( b ) tf = g , i ( a ) ...
... complex - valued function integrable over every compact subinterval of I. Let to I , and let co , C1 , ... , C - 1 be an arbitrary set of n complex numbers . Then there exists a unique ƒ € A " ( I ) such that ( a ) ( b ) tf = g , i ( a ) ...
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