Linear Operators, Part 2 |
From inside the book
Results 1-3 of 71
Page 937
... theory , it is possible not only to give a satisfactory foundation for these subjects , but also to develop their principal results , and this we shall attempt to do . The topics discussed are group theory and the Peter - Weyl theorem ...
... theory , it is possible not only to give a satisfactory foundation for these subjects , but also to develop their principal results , and this we shall attempt to do . The topics discussed are group theory and the Peter - Weyl theorem ...
Page 1435
... theory in somewhat greater detail . 7. Qualitative Theory of the Spectrum It will be seen in this section how a variety of qualitative results concerning the spectrum of a formally self adjoint formal differential operator v may readily ...
... theory in somewhat greater detail . 7. Qualitative Theory of the Spectrum It will be seen in this section how a variety of qualitative results concerning the spectrum of a formally self adjoint formal differential operator v may readily ...
Page 1583
... theory of special functions , which we shall briefly touch upon later . However , the " spectral " theory which they had discovered was to wait until the first decade of this century before it was actively taken up again . It was Dini ...
... theory of special functions , which we shall briefly touch upon later . However , the " spectral " theory which they had discovered was to wait until the first decade of this century before it was actively taken up again . It was Dini ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
Copyright | |
36 other sections not shown
Other editions - View all
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