Open Access
Issue |
ESAIM: M2AN
Volume 57, Number 4, July-August 2023
|
|
---|---|---|
Page(s) | 2257 - 2282 | |
DOI | https://doi.org/10.1051/m2an/2023054 | |
Published online | 03 July 2023 |
- H. Bahouri, J.-Y. Chemin and R. Danchin, Fourier Analysis and Nonlinear Partial Differential Equations. Vol. 343 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer, Heidelberg (2011). [CrossRef] [Google Scholar]
- A.A. Balinsky and W.D. Evans, Spectral Analysis of Relativistic Operators. Imperial College Press, London (2011). [Google Scholar]
- S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and T.Ø. Sørensen, The electron density is smooth away from the nuclei. Comm. Math. Phys. 228 (2002) 401–415. [CrossRef] [MathSciNet] [Google Scholar]
- S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and T. Østergaard Sørensen, Sharp regularity results for Coulombic many-electron wave functions. Comm. Math. Phys. 255 (2005) 183–227. [CrossRef] [MathSciNet] [Google Scholar]
- S. Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and T. Østergaard Sørensen, Analytic structure of many-body Coulombic wave functions. Comm. Math. Phys. 289 (2009) 291–310. [CrossRef] [MathSciNet] [Google Scholar]
- R.L. Frank, E.H. Lieb and R. Seiringer, Hardy–Lieb–Thirring inequalities for fractional Schrödinger operators. J. Amer. Math. Soc. 21 (2008) 925–950. [Google Scholar]
- I.W. Herbst, Spectral theory of the operator (p2 + m2)1/2 − Ze2/r. Comm. Math. Phys. 53 (1977) 285–294. [CrossRef] [MathSciNet] [Google Scholar]
- M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and H. Stremnitzer, Local properties of Coulombic wave functions. Comm. Math. Phys. 163 (1994) 185–215. [CrossRef] [MathSciNet] [Google Scholar]
- M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof and T.Ø. Sørensen, Electron wavefunctions and densities for atoms. Ann. Henri Poincaré 2 (2001) 77–100. [CrossRef] [MathSciNet] [Google Scholar]
- M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, A. Laptev and J. Tidblom, Many-particle Hardy inequalities. J. Lond. Math. Soc. 77 (2008) 99–114. [CrossRef] [MathSciNet] [Google Scholar]
- W. Hunziker and I.M. Sigal, The quantum N-body problem. J. Math. Phys. 41 (2000) 3448–3510. [CrossRef] [MathSciNet] [Google Scholar]
- T. Kato, On the eigenfunctions of many-particle systems in quantum mechanics. Comm. Pure Appl. Math. 10 (1957) 151–177. [CrossRef] [MathSciNet] [Google Scholar]
- H.C. Kreusler and H. Yserentant, The mixed regularity of electronic wave functions in fractional order and weighted Sobolev spaces. Numer. Math. 121 (2012) 781–802. [CrossRef] [MathSciNet] [Google Scholar]
- E.H. Lieb and M. Loss, Analysis. Vol. 14 of Graduate Studies in Mathematics, 2nd edition. American Mathematical Society, Providence, RI (2001). [Google Scholar]
- R.E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations. Vol. 49 of Mathematical Surveys and Monographs. American Mathematical Society, Providence, RI (1997). [Google Scholar]
- P.R. Stinga, User’s guide to the fractional Laplacian and the method of semigroups, in Handbook of Fractional Calculus with Applications. Vol. 2. De Gruyter, Berlin (2019) 235–265. [Google Scholar]
- H. Yserentant, On the regularity of the electronic Schrödinger equation in Hilbert spaces of mixed derivatives. Numer. Math. 98 (2004) 731–759. [CrossRef] [MathSciNet] [Google Scholar]
- H. Yserentant, The hyperbolic cross space approximation of electronic wavefunctions. Numer. Math. 105 (2007) 659–690. [CrossRef] [MathSciNet] [Google Scholar]
- H. Yserentant, The mixed regularity of electronic wave functions multiplied by explicit correlation factors. ESAIM Math. Model. Numer. Anal. 45 (2011) 803–824. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.