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Function extended spaces. (English) Zbl 1267.92061

Summary: Extended function spaces defined over the real field are defined as vector spaces made by the Cartesian product of a real Euclidian space and a real function space. This construct is related to the Holographic Electronic Density Theorem and to the stereographic projection of quantum chemically related and well behaved functions in general. It permits to establish the basis for the Holographic General Function Theorem.

MSC:

92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
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[1] Besalú E., Carbó-Dorca R.: J. Chem. Theor. Comput. 8, 854–861 (2012)
[2] Bonnacorsi R., Scrocco E., Tomasi J.: J. Chem. Phys. 52, 5270–5284 (1970)
[3] Mezey P.G.: Mol. Phys. 96, 169–178 (1999)
[4] P.G. Mezey, in Topological Similarity of Molecules and the Consequences of the Holographic Electron Density Theorem, an Extension of the Hohenberg-Kohn Theorem, ed. by R. Carbó-Dorca, X. Gironés, P.G. Mezey Fundamentals of Molecular Similarity Kluwer (Academic–Plenum Press, New York, 2001), pp. 113–124
[5] Mezey P.G.: J. Math. Chem. 30, 299–303 (2001) · Zbl 1007.92504
[6] Carbó-Dorca R.: J. Math. Chem. 49, 2109–2115 (2011) · Zbl 1231.81093
[7] R. Carbó-Dorca, Quantum Quantitative Structure-Activity Relationships (QQSAR): A comprehensive discussion based on inward matrix products, employed as a tool to find approximate solutions of strictly positive linear systems and providing a qsar-quantum similarity measures connection. in Proceedings of European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000. Barcelona, Sep 11–14, 2000. ISBN-84-89925-70-4, pp. 1–31 (2000)
[8] Sen K., Carbó-Dorca R.: J. Mol. Struct. (Theochem) 501, 173–176 (2000)
[9] Carbó-Dorca R.: J. Mol. Struct. Theochem 537, 41–54 (2001)
[10] Carbó-Dorca R.: J. Math. Chem. 30, 227–245 (2001) · Zbl 1021.81010
[11] Carbó-Dorca R.: Int. J. Quantum Chem. 91, 607–617 (2003)
[12] Carbó-Dorca R.: J. Math. Chem. 47, 331–334 (2010) · Zbl 1200.81077
[13] Carbó-Dorca R., Van Damme S.: Afinidad. 64, 147–153 (2007)
[14] Carbó-Dorca R., Mercado L.D.: J. Comput. Chem. 31, 2195–2212 (2010)
[15] Sobolev S.L.: Math. Sb. 4, 471–497 (1938)
[16] Bach A., Amat L., Besalú E., Carbó-Dorca R., Ponec R.: J. Math. Chem. 28, 59–70 (2000) · Zbl 0996.81528
[17] Carbó-Dorca R., Besalú E.: Int. J. Quantum Chem. 88, 167–182 (2002)
[18] Carbó-Dorca R., Besalú E.: J. Math. Chem. 29, 3–19 (2001) · Zbl 0996.81012
[19] Thurston W.P.: Three-Dimensional Geometry and Topology. Princeton University Press, Princeton (1997) · Zbl 0873.57001
[20] M. Hazewinkel (ed.), Encyclopaedia of Mathematics, vol. 9 (Kluwer Academic Publishers, Dordrecht, 1992) · Zbl 0806.00007
[21] Boas M.L.: Mathematical Methods in the Physical Sciences. Wiley, Hoboken (2006) · Zbl 1088.00002
[22] Carbó-Dorca R., Besalú E.: J. Math. Chem. 50, 981–988 (2012) · Zbl 1244.92069
[23] E. Besalú, R. Carbó-Dorca, Softened Electrostatic Molecular Potentials. IQC Technical Report TR-2012-3. J. Mol. Graph. Mod. (in press)
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