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self-adjoint operator


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1: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions
Self-Adjoint and Symmetric Operators
Formally Self-Adjoint and Self-Adjoint Differential OperatorsSelf-Adjoint Extensions
Consider formally self-adjoint operators of the form …
Self-Adjoint Operators
2: 1.3 Determinants, Linear Operators, and Spectral Expansions
Self-Adjoint Operators on 𝐄 n
Real symmetric ( 𝐀 = 𝐀 T ) and Hermitian ( 𝐀 = 𝐀 H ) matrices are self-adjoint operators on 𝐄 n . The spectrum of such self-adjoint operators consists of their eigenvalues, λ i , i = 1 , 2 , , n , and all λ i . …
3: 18.36 Miscellaneous Polynomials
These results are proven in Everitt et al. (2004), via construction of a self-adjoint Sturm–Liouville operator which generates the L n ( k ) ( x ) polynomials, self-adjointness implying both orthogonality and completeness. … Completeness and orthogonality follow from the self-adjointness of the corresponding Schrödinger operator, Gómez-Ullate and Milson (2014), Marquette and Quesne (2013).
4: 18.39 Applications in the Physical Sciences
The nature of, and notations and common vocabulary for, the eigenvalues and eigenfunctions of self-adjoint second order differential operators is overviewed in §1.18. … noting that the ψ p , l ( r ) are real, follows from the fact that the Schrödinger operator of (18.39.28) is self-adjoint, or from the direct derivation of Dunkl (2003). …
5: Bibliography R
  • M. Reed and B. Simon (1975) Methods of Modern Mathematical Physics, Vol. 2, Fourier Analysis, Self-Adjointness. Academic Press, New York.
  • M. Reed and B. Simon (1978) Methods of Modern Mathematical Physics, Vol. 4, Analysis of Operators. Academic Press, New York.
  • S. Ritter (1998) On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators. Z. Angew. Math. Mech. 78 (1), pp. 66–72.
  • G. Rota, D. Kahaner, and A. Odlyzko (1973) On the foundations of combinatorial theory. VIII. Finite operator calculus. J. Math. Anal. Appl. 42, pp. 684–760.
  • J. Rushchitsky and S. Rushchitska (2000) On Simple Waves with Profiles in the form of some Special Functions—Chebyshev-Hermite, Mathieu, Whittaker—in Two-phase Media. In Differential Operators and Related Topics, Vol. I (Odessa, 1997), Operator Theory: Advances and Applications, Vol. 117, pp. 313–322.