Linear Operators, Part 2 |
From inside the book
Results 1-3 of 82
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 L1 ( l ) of vector- valued functions . Let M be the mapping in L ( ↳1⁄2 ) which maps the vector - valued function whose nth component has the Fourier transform g ( ) into the vector - valued function ...
... functions boundedly into the space L1 ( l ) of vector- valued functions . Let M be the mapping in L ( ↳1⁄2 ) which maps the vector - valued function whose nth component has the Fourier transform g ( ) 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 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
36 other sections not shown
Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain 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 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 subspace Suppose T₁ T₂ theory To(t topology tr(T transform unique unitary vanishes vector zero