Orthogonality Relations for Cardinal B-Splines over Bounded Intervals
Starting from the recently discovered orthogonality relations for cardinal B-splines over the real line we derive suitably modified bilinear forms providing orthonormality over bounded intervals. We conjecture that these bilinear forms are positive definite and therefore inner products for B-splines of arbitrary order n ∈ IN. For n ≤ 8, this is verified by explicit computation of the corresponding matrices. Further, applications to approximation theory are discussed.
KeywordsBilinear Form Orthogonality Relation Bound Interval Minimal Eigenvalue Weighted Sobolev Space
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