Linear Operators, Part 2 |
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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 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 ...
Page 1634
... theory . As the complexity of the basic elementary expression ( 1 ) makes clear , the mere notation for partial ... theory of distributions , to which Section 3 below will be devoted . Once generalized derivatives in the sense of the ...
... theory . As the complexity of the basic elementary expression ( 1 ) makes clear , the mere notation for partial ... theory of distributions , to which Section 3 below will be devoted . Once generalized derivatives in the sense of the ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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Common terms and phrases
adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense 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 linear 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 subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero