{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T23:01:32Z","timestamp":1782169292698,"version":"3.54.5"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2004,8,6]],"date-time":"2004-08-06T00:00:00Z","timestamp":1091750400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2004,10]]},"DOI":"10.1007\/s00211-003-0498-1","type":"journal-article","created":{"date-parts":[[2004,8,5]],"date-time":"2004-08-05T09:25:41Z","timestamp":1091697941000},"page":"731-759","source":"Crossref","is-referenced-by-count":59,"title":["On the regularity of the electronic Schr\ufffddinger equation in Hilbert spaces of mixed derivatives"],"prefix":"10.1007","volume":"98","author":[{"given":"Harry","family":"Yserentant","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2004,8,6]]},"reference":[{"key":"CR1","first-page":"672","volume":"1","author":"Babenko","year":"1960","unstructured":"Babenko, K.I.: Approximation by trigonometric polynomials in a certain class of periodic functions of several variables. Soviet Math. Dokl. 1, 672?675 (1960)","journal-title":"Soviet Math. Dokl."},{"key":"CR2","unstructured":"Bungartz, H.J.: Finite Elements of Higher Order on Sparse Grids, Habilitationsschrift, Fakult\u00e4t f\u00fcr Informatik, TU M\u00fcnchen. Aachen: Shaker Verlag 1998"},{"key":"CR3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s003659900060","volume":"14","author":"DeVore","year":"1998","unstructured":"DeVore, R.A., Konyagin, S.V., Temlyakov, V.N.: Hyperbolic wavelet approximation. Constr. Approx. 14, 1?26 (1998)","journal-title":"Constr. Approx."},{"key":"CR4","first-page":"9461","volume":"116","author":"Flad","year":"2002","unstructured":"Flad, H.J., Hackbusch, W., Kolb, D., Schneider, R.: Wavelet approximation of correlated wave functions. I. Basics. J. Chem. Phys. 116, 9461?9657 (2002)","journal-title":"I. Basics. J. Chem. Phys."},{"key":"CR5","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1007\/s002200200668","volume":"228","author":"Fournais","year":"2002","unstructured":"Fournais, S., Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T., \u00d8stergard S\u00f8rensen, T.: The electron density is smooth away from the nuclei. Commun. Math. Phys. 228, 401?415 (2002)","journal-title":"Commun. Math. Phys."},{"key":"CR6","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1006\/jcph.2000.6627","volume":"165","author":"Garcke","year":"2000","unstructured":"Garcke, J., Griebel, M.: On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique. J. Comput. Phys. 165, 694?716 (2000)","journal-title":"J. Comput. Phys."},{"key":"CR7","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1007\/s003650010010","volume":"16","author":"Griebel","year":"2000","unstructured":"Griebel, M., Knapek, S.: Optimized tensor-product approximation spaces. Constr. Approx. 16, 525?540 (2000)","journal-title":"Constr. Approx."},{"key":"CR8","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/s006070170015","volume":"67","author":"Hackbusch","year":"2000","unstructured":"Hackbusch, W.: The efficient computation of certain determinants arising in the treatment of Schr\u00f6dinger?s equation. Computing 67, 35?56 (2000)","journal-title":"Computing"},{"key":"CR9","unstructured":"Helgaker, T., J\u00f8rgensen, P., Olsen, J.: Molecular electronic structure theory. New York: John Wiley and Sons, 2001"},{"key":"CR10","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/PL00001033","volume":"2","author":"Hoffmann-Ostenhof","year":"2001","unstructured":"Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T., \u00d8stergard S\u00f8rensen, T.: Electron wavefunctions and densities for atoms. Ann. Henri Poincar\u00e9 2, 77?100 (2001)","journal-title":"Ann. Henri Poincar\u00e9"},{"key":"CR11","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1007\/BF02101740","volume":"163","author":"Hoffmann-Ostenhof","year":"1994","unstructured":"Hoffmann-Ostenhof, M., Hoffmann-Ostenhof, T., Stremnitzer, H.: Local properties of coulombic wave functions. Commun. Math. Phys. 163, 185?215 (1994)","journal-title":"Commun. Math. Phys."},{"key":"CR12","doi-asserted-by":"crossref","first-page":"3448","DOI":"10.1063\/1.533319","volume":"41","author":"Hunziker","year":"2000","unstructured":"Hunziker, W., Sigal, I. M.: The quantum N-body problem. J. Math. Phys. 41, 3448?3510 (2000)","journal-title":"J. Math. Phys."},{"key":"CR13","first-page":"3625","volume":"117","author":"Luo","year":"2002","unstructured":"Luo, H., Kolb, D., Flad, H.J, Hackbusch, W., Koprucki, T.: Wavelet approximation of correlated wave functions. II. Hyperbolic wavelets and adaptive approximation schemes. J. Chem. Phys. 117, 3625?3638 (2002)","journal-title":"II. Hyperbolic wavelets and adaptive approximation schemes. J. Chem. Phys."},{"key":"CR14","first-page":"195","volume":"70","author":"Kato","year":"1951","unstructured":"Kato, T.: Fundamental properties of Hamiltonian operators of Schr\u00f6dinger type. Trans. Am. Math. Soc. 70, 195?221 (1951)","journal-title":"Trans. Am. Math. Soc."},{"key":"CR15","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1002\/cpa.3160100201","volume":"10","author":"Kato","year":"1957","unstructured":"Kato, T.: On the eigenfunctions of many-particle systems in quantum mechanics. Commun. Pure and Appl. Math. 10, 151?177 (1957)","journal-title":"Commun. Pure and Appl. Math."},{"key":"CR16","unstructured":"Parr, R.G., Yang, W.: Density-Functional Theory of Atoms and Molecules. Oxford: Oxford University Press, 1994"},{"key":"CR17","unstructured":"Reed, M., Simon, B.: Methods of Modern Mathematical Physics IV: Analysis of Operators. San Diego: Academic Press, 1978"},{"key":"CR18","doi-asserted-by":"crossref","first-page":"3523","DOI":"10.1063\/1.533321","volume":"41","author":"Simon","year":"2000","unstructured":"Simon, B.: Schr\u00f6dinger operators in the twentieth century. J. Math. Phys. 41, 3523?3555 (2000)","journal-title":"J. Math. Phys."},{"key":"CR19","first-page":"240","volume":"4","author":"Smolyak","year":"1963","unstructured":"Smolyak, S.A.: Quadrature and interpolation formulas for tensor products of certain classes of functions. Dokl. Akad. Nauk SSSR 4, 240?243 (1963)","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"CR20","unstructured":"Szabo, A., Ostlund, N.S.: Modern Quantum Chemistry, Introduction to Advanced Electronic Structure Theory. New York: Dover Publications, 1996"},{"key":"CR21","unstructured":"von Neumann, J.: Mathematische Grundlagen der Quantenmechanik. Berlin: Springer-Verlag, 1932"},{"key":"CR22","unstructured":"Yserentant, H.: On the electronic Schr\u00f6dinger equation. Lecture Notes, Universit\u00e4t T\u00fcbingen 2003; accessible via http:\/\/na.uni-tuebingen.de"},{"key":"CR23","unstructured":"Zenger, C.: Sparse grids. In: W. Hackbusch (ed.) Parallel Algorithms for Partial Differential Equations. Proceedings, Kiel 1990, pp. 241?251. Notes on Numerical Fluid Mechanics vol. 31, Braunschweig Wiesbaden: Vieweg, 1991"}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-003-0498-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-003-0498-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-003-0498-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T12:22:34Z","timestamp":1558614154000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-003-0498-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,8,6]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,10]]}},"alternative-id":["498"],"URL":"https:\/\/doi.org\/10.1007\/s00211-003-0498-1","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,8,6]]}}}