1982
DOI: 10.1070/sm1982v043n04abeh002581
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Asymptotics of Singular Numbers of Imbedding Operators for Certain Classes of Analytic Functions

Abstract: By separating the total energy of atoms and diatomic molecules into the sum of Thomas-Fermi, density gradient and exchange energies, the dissociation energy D, divided by the square of the total number of electrons in the molecule, is related by a simple analytic formula to the inhomogeneity kinetic energy of electron gas theory, for the equilibrium molecule. The shape of the resulting relation has the features of a semi-empirical correlation previously established.

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Cited by 18 publications
(27 citation statements)
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“…Remark. (a) Under the stated hypotheses we have l n Bcp n ; for positive constants c; and po1; in view of results of Parfenov [23]. Therefore the hypothesis in Theorem 3.1 is equivalent to…”
Section: Analytic Continuation Via Eigenfunction Expansionmentioning
confidence: 91%
See 1 more Smart Citation
“…Remark. (a) Under the stated hypotheses we have l n Bcp n ; for positive constants c; and po1; in view of results of Parfenov [23]. Therefore the hypothesis in Theorem 3.1 is equivalent to…”
Section: Analytic Continuation Via Eigenfunction Expansionmentioning
confidence: 91%
“…its eigenvalues. Actually, it is not hard to prove that the eigenvalues l n decay exponentially, in the sense that lim sup l 1=n n o1; see [23] or [20,22]. The corresponding eigenfunctions f n AAL 2 ðO 1 Þ; nX0; satisfy the identity Z…”
Section: Introductionmentioning
confidence: 99%
“…We have obtained the following proposition. The operatorS differs from the multiplication by z by a rank-one operator: S − S = (·, g)(1 − θ), for the norm of which we have (7) S…”
Section: The Spaces K θ and The Model Constructionmentioning
confidence: 99%
“…For a sign-definite symbol, in the complex Bargmann case, rather complete results were obtained in [14], [11] and, in dimension d = 1, improved in [6], see also references therein. Even earlier, the case of complex Bergman spaces in dimension d = 1 has been studied in [12]. It was proved that the eigenvalues of the Toeplitz operator follow an asymptotic law, of an exponential type for the Bergman case and super-exponential type for the Bargmann one.…”
Section: Introductionmentioning
confidence: 99%