TY - JOUR

T1 - Regular Hermite Interpolation in an Arbitrary Connected Open Subset of a Topological Vector Space

AU - Evard, J. Cl

AU - Jafari, F.

PY - 1995/6/15

Y1 - 1995/6/15

N2 - We establish the existence of regular Hermite interpolations in an arbitrary connected open subset S of a topological vector space E: given N points x10, …, xN0 in S and given directions xki ∈ E for all k ∈ {1, …, N}, i ∈ {1, …, m} such that xkl ≠ 0, we prove that there exists an E-polynomial p:R → E with values in S such that p(i)(k) = xki ∀k ∈ {1, …, N}, i ∈ {0, …, m}, p(t) ∈ S, p′(t) ≠ 0 ∀t ∈ [l, N].

AB - We establish the existence of regular Hermite interpolations in an arbitrary connected open subset S of a topological vector space E: given N points x10, …, xN0 in S and given directions xki ∈ E for all k ∈ {1, …, N}, i ∈ {1, …, m} such that xkl ≠ 0, we prove that there exists an E-polynomial p:R → E with values in S such that p(i)(k) = xki ∀k ∈ {1, …, N}, i ∈ {0, …, m}, p(t) ∈ S, p′(t) ≠ 0 ∀t ∈ [l, N].

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U2 - 10.1006/jmaa.1995.1207

DO - 10.1006/jmaa.1995.1207

M3 - Article

AN - SCOPUS:58149366119

SN - 0022-247X

VL - 192

SP - 841

EP - 854

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 3

ER -