## Linear Operators: Spectral theory |

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Page 939

Theorem

that L*x* = x* for every s in G. It ... Now, if (is is defined by the equation fit(E)=/,t(s~

1E) then, since x* = x*La, we have jGf(t)(i(dt) = jGf(st)

Theorem

**V**.10.8 may now be applied to yield the existence of a point x* in K suchthat L*x* = x* for every s in G. It ... Now, if (is is defined by the equation fit(E)=/,t(s~

1E) then, since x* = x*La, we have jGf(t)(i(dt) = jGf(st)

**fi**(dt) = jgf(t)p,(dt), f e C(G).Page 1211

Under Hypothesis 7, there is, for each g in L2(S, E,

Cartesian product of S and the real number system R which is measurable with

respect ... The B-space adjoint A* of An maps L^a(Sn,

Under Hypothesis 7, there is, for each g in L2(S, E,

**v**), a function W defined on theCartesian product of S and the real number system R which is measurable with

respect ... The B-space adjoint A* of An maps L^a(Sn,

**v**) = L**(Sn,**v**) into L2(en,**fi**).Page 1928

... b] to [a, 6J. line 9: Insert before vector: countably additive. line 6: Change /„ to /

B<. line 2: Change 8 to 2. line 16: Change /„ to /„ . line 5: Change |/B(*)» to |/.(t)|».

line 3: Change oo to 0. Change the second -> in the line to = . line 7: Change

...

... b] to [a, 6J. line 9: Insert before vector: countably additive. line 6: Change /„ to /

B<. line 2: Change 8 to 2. line 16: Change /„ to /„ . line 5: Change |/B(*)» to |/.(t)|».

line 3: Change oo to 0. Change the second -> in the line to = . line 7: Change

**v**(**fi**,...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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Acad adjoint extension adjoint operator algebra Amer analytic B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant 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 q Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma Proc prove real axis real numbers representation satisfies Section sequence singular solution spectral spectral theory square-integrable subspace Suppose symmetric operator theory topology transform unique unitary vanishes vector zero