Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
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Page 1272
... indices are d o , d_ The operator T1 is called an elementary symmetric operator . It may be proved that if T is maximal symmetric with indices d = 0 , d_ = n ( where n is any cardinal number ) , then may be broken into a direct sum of ...
... indices are d o , d_ The operator T1 is called an elementary symmetric operator . It may be proved that if T is maximal symmetric with indices d = 0 , d_ = n ( where n is any cardinal number ) , then may be broken into a direct sum of ...
Page 1398
... indices of To ( T ) is k , then for λ & o , ( T ) the equation to = λo has at least λσ k linearly independent solutions in L¿ ( 1 ) . PROOF . By Theorem 2.10 and XII.4.7 ( c ) , the adjoint of To ( T ) is T1 ( 7 ) . The desired result ...
... indices of To ( T ) is k , then for λ & o , ( T ) the equation to = λo has at least λσ k linearly independent solutions in L¿ ( 1 ) . PROOF . By Theorem 2.10 and XII.4.7 ( c ) , the adjoint of To ( T ) is T1 ( 7 ) . The desired result ...
Page 1611
... indices of 7 are equal ( 6.6 ) . ( 2 ) In particular , the deficiency indices are equal if 7 is bounded below . ( 3 ) If for some real or complex 2 all solutions of the equation ( λ − t ) f = 0 are square - integrable , then the ...
... indices of 7 are equal ( 6.6 ) . ( 2 ) In particular , the deficiency indices are equal if 7 is bounded below . ( 3 ) If for some real or complex 2 all solutions of the equation ( λ − t ) f = 0 are square - integrable , then the ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients compact subset complex numbers continuous function converges Corollary deficiency indices Definition denote dense domain eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood norm open set open subset orthonormal partial differential operator Plancherel's theorem positive PROOF prove real axis real numbers satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose T₁ T₁(t theory To(t topology unique unitary vanishes vector zero