Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 891
Nelson Dunford, Jacob T. Schwartz. scalar function f with respect to the operator valued set function E. In the present chapter we shall only integrate bounded functions f and so the following discussion of the integral will be ...
Nelson Dunford, Jacob T. Schwartz. scalar function f with respect to the operator valued set function E. In the present chapter we shall only integrate bounded functions f and so the following discussion of the integral will be ...
Page 1178
... functions boundedly into the space L ( 2 ) of vector- valued functions . Let M be the mapping in L ( 2 ) which maps the vector - valued function whose nth component has the Fourier transform g ( ) into the vector - valued function whose ...
... functions boundedly into the space L ( 2 ) of vector- valued functions . Let M be the mapping in L ( 2 ) which maps the vector - valued function whose nth component has the Fourier transform g ( ) into the vector - valued function whose ...
Page 1922
... function , III.5.15 ( 140 ) of a set function , III.1.4 ( 97 ) . ( See also Variation ) Totally ordered set , I.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ( 515 ) , XI.6.8 ( 1016 ) of a matrix , definition , VI.9.28 ( 515 ) of two ...
... function , III.5.15 ( 140 ) of a set function , III.1.4 ( 97 ) . ( See also Variation ) Totally ordered set , I.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ( 515 ) , XI.6.8 ( 1016 ) of a matrix , definition , VI.9.28 ( 515 ) of two ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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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 compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero