Piecewise polynomials with different smoothness degrees on polyhedral complexes

Date

2019-05-01

Author

ALTINOK BHUPAL, SELMA
Sipahi, Neslihan Os

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

198
views

0
downloads

For a given d-dimensional polyhedral complex Delta and a given degree k, we consider the vector space of piecewise polynomial functions on Delta of degree at most k with a different smoothness condition on each pair of adjacent d-faces of Delta. This is a finite dimensional vector space. The fundamental problem in Approximation Theory is to compute the dimension of this vector space. It is known that the dimension is given by a polynomial for sufficiently large k via commutative algebra. By using the technique of McDonald and Schenck [3] and extending their result to a plane polyhedral complex Delta with varying smoothness conditions, we determine this polynomial. This gives a complete answer for the dimension. At the end we discuss some examples through this technique.

Subject Keywords

Mathematics (miscellaneous)

URI

https://hdl.handle.net/11511/65897

Journal

QUAESTIONES MATHEMATICAE

DOI

https://doi.org/10.2989/16073606.2018.1481464

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Invariant subspaces for Banach space operators with an annular spectral set Yavuz, Onur (2008-01-01) Consider an annulus Omega = {z epsilon C : r(0) 0 such that parallel to p(T)parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} and parallel to p(r(0)T(-1))parallel to <= K sup{vertical bar p(lambda)vertical bar : vertical bar lambda vertical bar <= 1} for all polynomials p. Then there exists a nontrivial common invariant subspace for T* and T*(-1).
Displaceability of Certain Constant Sectional Curvature Lagrangian Submanifolds Şirikçi, Nil İpek (Springer Science and Business Media LLC, 2020-10-01) We present an alternative proof of a nonexistence result for displaceable constant sectional curvature Lagrangian submanifolds under certain assumptions on the Lagrangian submanifold and on the ambient symplectically aspherical symplectic manifold. The proof utilizes an index relation relating the Maslov index, the Morse index and the Conley-Zehnder index for a periodic orbit of the flow of a specific Hamiltonian function, a result on this orbit's Conley-Zehnder index and another result on the Morse indices...
Concrete description of CD0(K)-spaces as C(X)-spaces and its applications Ercan, Z (American Mathematical Society (AMS), 2004-01-01) We prove that for a compact Hausdorff space K without isolated points, CD0(K) and C(K x {0, 1}) are isometrically Riesz isomorphic spaces under a certain topology on K x {0, 1}. Moreover, K is a closed subspace of K x {0, 1}. This provides concrete examples of compact Hausdorff spaces X such that the Dedekind completion of C(X) is B(S) (= the set of all bounded real-valued functions on S) since the Dedekind completion of CD0(K) is B(K) (CD0(K, E) and CDw (K, E) spaces as Banach lattices).
Unified treatment of spacelike and timelike SO(3,1) Yang-Mills fields Dundarer, AR (Springer Science and Business Media LLC, 2001-07-01) SO(3, 1) valued Yang-mills fields stemming from spacelike and timelike vectors that were studied separately in earlier works are unified by introducing a parameter lambda that takes values in the interval [-1, 1].
Polynomial solution of non-central potentials Ikhdair, Sameer M.; Sever, Ramazan (Springer Science and Business Media LLC, 2007-10-01) We show that the exact energy eigenvalues and eigenfunctions of the Schrodinger equation for charged particles moving in certain class of non-central potentials can be easily calculated analytically in a simple and elegant manner by using Nikiforov and Uvarov (NU) method. We discuss the generalized Coulomb and harmonic oscillator systems. We study the Hartmann Coulomb and the ring-shaped and compound Coulomb plus Aharanov-Bohm potentials as special cases. The results are in exact agreement with other methods.

Citation Formats

S. ALTINOK BHUPAL and N. O. Sipahi, “Piecewise polynomials with different smoothness degrees on polyhedral complexes,” QUAESTIONES MATHEMATICAE, pp. 673–685, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65897.