## Linear Operators: Spectral theory |

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Page 926

Notes and Remarks The basic result of this chapter concerning the spectral

this result were also given by F. Riesz [ 20 , 6 ] , and contributions were made by

many ...

Notes and Remarks The basic result of this chapter concerning the spectral

**theory**of Hermitian operators goes back to the work of Hilbert [ 1 , IV ) . Proofs ofthis result were also given by F. Riesz [ 20 , 6 ] , and contributions were made by

many ...

Page 937

CHAPTER XI Miscellaneous Applications This chapter is devoted to applications

of the spectral

mathematics . Since these topics are not in the main stream of our interest we

shall ...

CHAPTER XI Miscellaneous Applications This chapter is devoted to applications

of the spectral

**theory**of normal operators to problems in a variety of fields ofmathematics . Since these topics are not in the main stream of our interest we

shall ...

Page 1804

Spectral

16 . The reduction problem in spectral

. , Cambridge , Mass . , 1950 , Vol . 2 , 115–122 . 17 . Spectral

Spectral

**theory**. Proc . Symposium on Spectral**Theory**etc. , 203–208 ( 1951 ) .16 . The reduction problem in spectral

**theory**. Proc . International Congress Math. , Cambridge , Mass . , 1950 , Vol . 2 , 115–122 . 17 . Spectral

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additive adjoint operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero