Quasi-splines and their moduli

Journal de Mathématiques Pures et Appliquées - Tập 104 - Trang 1-28 - 2015
Patrick Clarke1
1Department of Mathematics, Drexel University, Philadelphia, PA 19104, United States

Tài liệu tham khảo

Billera, 1991, A dimension series for multivariate splines, Discrete Comput. Geom., 6, 107, 10.1007/BF02574678 Grothendieck, 1961, Éléments de géométrie algébrique. II. Étude globale élémentaire de quelques classes de morphismes, Publ. Math. IHÉS, 222 Hrennikoff, 1941, Solution of problems of elasticity by the framework method, J. Appl. Mech., 8, A-169, 10.1115/1.4009129 Courant, 1943, Variational methods for the solution of problems of equilibrium and vibrations, Bull. Am. Math. Soc., 49, 1, 10.1090/S0002-9904-1943-07818-4 Schoenberg, 1946, Contributions to the problem of approximation of equidistant data by analytic functions. Part A. On the problem of smoothing or graduation. A first class of analytic approximation formulae, Q. Appl. Math., 4, 45, 10.1090/qam/15914 de Casteljau, 1959 Farin, 1977 Alfeld, 1987, The dimension of bivariate spline spaces of smoothness r for degree d≥4r+1, Constr. Approx., 3, 189, 10.1007/BF01890563 Alfeld, 1990, On the dimension of bivariate spline spaces of smoothness r and degree d=3r+1, Numer. Math., 57, 651, 10.1007/BF01386434 Alfeld, 1993, The generic dimension of the space of C1 splines of degree d≥8 on tetrahedral decompositions, SIAM J. Numer. Anal., 30, 889, 10.1137/0730047 Möbius, 1827 Bernstein, 1912, Démonstration du théorème de Weierstrauss, fondée sur le calcul des probabilités, Comm. Soc. Math. Kharkov, 13 Weierstrass, 1885, Über die analytische Darstellbarkeit sogenannter willkürlicher Functionen einer reellen Veränderlichen, Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften zu Berlin, II Lai, 2007, Spline Functions on Triangulations, vol. 110 Schumaker, 1979, On the dimension of spaces of piecewise polynomials in two variables, vol. 51, 396 Billera, 1988, Homology of smooth splines: generic triangulations and a conjecture of Strang, Trans. Am. Math. Soc., 310, 325, 10.1090/S0002-9947-1988-0965757-9 Strang, 1974, The dimension of piecewise polynomial spaces, and one-sided approximation, vol. 363, 144 Schenck, 1997, A spectral sequence for splines, Adv. Appl. Math., 19, 183, 10.1006/aama.1997.0534 Schenck, 1997, Local cohomology of bivariate splines, J. Pure Appl. Algebra, 117/118, 535, 10.1016/S0022-4049(97)00026-1 Billera, 1989, Gröbner basis methods for multivariate splines, 93 Yuzvinsky, 1992, Modules of splines on polyhedral complexes, Math. Z., 210, 245, 10.1007/BF02571795 Schenck, 2014, Splines on the Alfeld split of a simplex and type A root systems, J. Approx. Theory, 182, 1, 10.1016/j.jat.2014.02.005 Foucart, 2013, Generating dimension formulas for multivariate splines, Albanian J. Math., 7, 25 Stiller, 1983, Certain reflexive sheaves on PCn and a problem in approximation theory, Trans. Am. Math. Soc., 279, 125 Iarrobino, 1997, Inverse system of a symbolic power. III. Thin algebras and fat points, Compos. Math., 108, 319, 10.1023/A:1000155612073 Geramita, 1997, Fat points, inverse systems and piecewise polynomial functions, vol. 105, 98 Schenck, 2002, Cohomology vanishing and a problem in approximation theory, Manuscr. Math., 107, 43, 10.1007/s002290100222 Billera, 1992, Modules of piecewise polynomials and their freeness, Math. Z., 209, 485, 10.1007/BF02570848 Gilbert Bifet, 1990, Cohomology of regular embeddings, Adv. Math., 82, 1, 10.1016/0001-8708(90)90082-X Brion, 1997, Equivariant Chow groups for torus actions, Transform. Groups, 2, 225, 10.1007/BF01234659 Goresky, 1998, Equivariant cohomology, Koszul duality, and the localization theorem, Invent. Math., 131, 25, 10.1007/s002220050197 Payne, 2006, Equivariant Chow cohomology of toric varieties, Math. Res. Lett., 13, 29, 10.4310/MRL.2006.v13.n1.a3 Schenck, 2012, Equivariant chow cohomology of nonsimplicial toric varieties, Trans. Am. Math. Soc., 364, 4041, 10.1090/S0002-9947-2012-05409-2 Serre, 1955, Faisceaux algébriques cohérents, Ann. of Math. (2), 61, 197, 10.2307/1969915 Hartshorne, 1977, Algebraic Geometry, vol. 52 Grothendieck, 1963, Éléments de géométrie algébrique. III. Étude cohomologique des faisceaux cohérents. II, Publ. Math. IHÉS, 91 Mumford, 1966, Lectures on Curves on an Algebraic Surface, vol. 59 Gotzmann, 1978, Eine Bedingung für die Flachheit und das Hilbertpolynom eines graduierten Ringes, Math. Z., 158, 61, 10.1007/BF01214566 Bruns, 1993, Cohen–Macaulay Rings, vol. 39 Grothendieck, 1960-1961, Techniques de construction et théorèmes d'existence en géométrie algébrique. IV. Les schémas de Hilbert Stacks Project Authors