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Page 854
... applications is different from that of Stone . We are indebted to many students and colleagues for calling our attention to misprints and errors that have occurred in Part I. Such corrections appear in a list of errata . We wish to ...
... applications is different from that of Stone . We are indebted to many students and colleagues for calling our attention to misprints and errors that have occurred in Part I. Such corrections appear in a list of errata . We wish to ...
Page 937
Nelson Dunford, Jacob T. Schwartz. CHAPTER XI Miscellaneous Applications This chapter is devoted to applications of the spectral theory of normal operators to problems in a variety of fields of mathematics . Since these topics are not in ...
Nelson Dunford, Jacob T. Schwartz. CHAPTER XI Miscellaneous Applications This chapter is devoted to applications of the spectral theory of normal operators to problems in a variety of fields of mathematics . Since these topics are not in ...
Page 1831
... applications , I , II . I. Mat . Sbornik N. S. 20 ( 62 ) , 431-495 ( 1947 ) . II . ibid . 21 ( 63 ) , 365–404 ( 1947 ) . ( Russian ) Math . Rev. 9 , 515–516 ( 1948 ) . Sur les fonctions de Green non - symétriques oscillatoires des ...
... applications , I , II . I. Mat . Sbornik N. S. 20 ( 62 ) , 431-495 ( 1947 ) . II . ibid . 21 ( 63 ) , 365–404 ( 1947 ) . ( Russian ) Math . Rev. 9 , 515–516 ( 1948 ) . Sur les fonctions de Green non - symétriques oscillatoires des ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 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 PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero