Linear Operators: Spectral theory |
From inside the book
Results 1-3 of 91
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 978
... applications are to be found in Section 5. A deep insight into the L1 - closure theory may be obtained by a study of A. Beurling's problem of spectral synthesis which is also discussed in this section . This is the problem of ...
... applications are to be found in Section 5. A deep insight into the L1 - closure theory may be obtained by a study of A. Beurling's problem of spectral synthesis which is also discussed in this section . This is the problem of ...
Page 1165
... applications of their results to a number of " potential " kernels of the sort arising in the theory of partial differential equations . Subsequently their inequality has found many important applications in this theory . In [ 5 ] ...
... applications of their results to a number of " potential " kernels of the sort arising in the theory of partial differential equations . Subsequently their inequality has found many important applications in this theory . In [ 5 ] ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Copyright | |
59 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 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 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 real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology tr(T unique unitary vanishes vector zero