Linear Operators: Spectral theory |
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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 ( § ) into the vector - valued function ...
... 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 ( § ) into the vector - valued function ...
Page 1645
... functions , but can only be a " function " in some generalized sense . Hence , we are led to the attempt to define some sort of " generalized function . " A very complete and interesting development of such a theory of generalized functions ...
... functions , but can only be a " function " in some generalized sense . Hence , we are led to the attempt to define some sort of " generalized function . " A very complete and interesting development of such a theory of generalized functions ...
Contents
BAlgebras | 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 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