## Linear Operators: Spectral theory |

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Page 940

The function f is said to be

The function f is said to be

**finite dimensional**if its set { fs seG ) of translates is a**finite dimensional**vector space of functions , The spectral theorem will be used in the proof of the following theorem and so the field of scalars ...Page 1092

By Lemma 5 and Corollary 4 , and the elementary fact that any compact operator may be approximated in norm by a sequence of operators In with

By Lemma 5 and Corollary 4 , and the elementary fact that any compact operator may be approximated in norm by a sequence of operators In with

**finitedimensional**range , it is enough to prove the lemma in the special case that T has ...Page 1146

Any

Any

**finite dimensional**representation of a compact group G is a direct sum of irreducible representations . This theorem shows that in studying**finite dimensional**representations of a compact group G we may , without loss of generality ...### What people are saying - Write a review

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### Contents

8 | 876 |

859 | 885 |

extensive presentation of applications of the spectral theorem | 911 |

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additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero