Linear Operators, Part 2Interscience Publishers, 1963 - Algebra, Universal |
From inside the book
Results 1-3 of 61
Page 1272
... deficiency indices are different from zero . A maximal symmetric operator is one which has no proper symmetric extensions ; hence , a closed symmetric operator is maximal if at least one of its deficiency indices is zero . If both are ...
... deficiency indices are different from zero . A maximal symmetric operator is one which has no proper symmetric extensions ; hence , a closed symmetric operator is maximal if at least one of its deficiency indices is zero . If both are ...
Page 1398
... deficiency 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 ...
... deficiency 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 ...
Page 1611
... deficiency 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 ...
... deficiency 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 ...
Contents
IX | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
25 other sections not shown
Other editions - View all
Common terms and phrases
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