Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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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 of regular and irregular singularities enables us to reduce the problem of determining the deficiency indices of 7 to a finite algebraic problem . We will return to the ... THEORY OF THE SPECTRUM Qualitative Theory of the Spectrum.
... theory of regular and irregular singularities enables us to reduce the problem of determining the deficiency indices of 7 to a finite algebraic problem . We will return to the ... THEORY OF THE SPECTRUM Qualitative Theory of the Spectrum.
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 |
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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach Banach spaces Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists follows from Lemma follows immediately formal differential operator formally self adjoint formula 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 linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal positive Proc PROOF prove real axis satisfies sequence singular solution spectral spectral theory square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero