Smoothness as an invariant property of coefficients of linear differential equations
František Neuman (1989)
Czechoslovak Mathematical Journal
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František Neuman (1989)
Czechoslovak Mathematical Journal
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Verdoodt, Ann (1994)
Bulletin of the Belgian Mathematical Society - Simon Stevin
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Haddad, L., Helou, C., Pihko, J. (2005)
International Journal of Mathematics and Mathematical Sciences
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Edoardo Ballico (2005)
Open Mathematics
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Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(nn+x). Here we prove that the order x Veronese embedding ofP n is not weakly (k−1)-defective, i.e. for a general S⊃P n such that #(S) = k+1 the projective space | I 2S (x)| of all degree t hypersurfaces ofP n singular at each point of S has dimension (n/n+x )−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I 2S (x)| has an ordinary double point at each P∈ S and Sing (F)=S.
Suárez, C. (2010)
Advances in Difference Equations [electronic only]
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Bouchard, Pierre, Chang, Hungyung, Ma, Jun, Yeh, Jean, Yeh, Yeong-Nan (2010)
The Electronic Journal of Combinatorics [electronic only]
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Chattopadhyay, Rita (1987)
International Journal of Mathematics and Mathematical Sciences
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Jung, Hee Sun, Sakai, Ryozi (2009)
Journal of Inequalities and Applications [electronic only]
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Sulaiman, W.T. (2011)
Journal of Inequalities and Applications [electronic only]
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Sulaiman, W.T. (1999)
Portugaliae Mathematica
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Adam Lecko (2000)
Annales Polonici Mathematici
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Some inequalities are proved for coefficients of functions in the class P(α), where α ∈ [0,1), of functions with real part greater than α. In particular, new inequalities for coefficients in the Carathéodory class P(0) are given.