## Linear Operators: Spectral theory |

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Page 1239

Conversely, let T be a self

restriction of To to a subspace Q3 of Q(T*) determined by a symmetric family of

linearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

Conversely, let T be a self

**adjoint extension**of T. Then by Lemma 26, T, is therestriction of To to a subspace Q3 of Q(T*) determined by a symmetric family of

linearly independent boundary conditions B, (a) = 0, i = 1,..., k, and we have only

to ...

Page 1270

The problem of determining whether a given symmetric operator has a self

affirmative, it is important to know what the self

how they ...

The problem of determining whether a given symmetric operator has a self

**adjoint extension**is of crucial importance in ... If the answer to this problem isaffirmative, it is important to know what the self

**adjoint extensions**look like andhow they ...

Page 1622

Borg showed that, given the distribution of eigenvalues for two self

, and proved that the distribution of eigenvalues of one self

Borg showed that, given the distribution of eigenvalues for two self

**adjoint****extensions**of the operator d \? - - - - t), ... Levinson [4] simplified Borg's arguments, and proved that the distribution of eigenvalues of one self

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Spectral Representation | 909 |

Copyright | |

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adjoint extension adjoint operator algebra Amer analytic B-algebra Banach Borel set boundary conditions boundary values bounded operator closed closure Cº(I coefficients complete complex numbers continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel Lemma Let f linear operator linearly independent mapping Math matrix measure Nauk SSSR N.S. neighborhood norm open set operators in Hilbert orthogonal orthonormal Plancherel's theorem positive Proc PRoof prove real numbers satisfies sequence singular ſº solution spectral spectral set spectral theory square-integrable subspace Suppose theory To(r topology transform unique unitary vanishes vector zero