Polynomial splines and eigenvalue approximations on quantum graphs |
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Authors: | Isaac Pesenson |
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Institution: | Department of Mathematics, Temple University, Philadelphia, PA 19122, USA |
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Abstract: | A notion of splines is introduced on a quantum graph Γ. It is shown that eigen values of a Hamiltonian on a finite graph Γ can be determined as limits of eigenvalues of certain finite-dimensional operators in spaces of polynomial splines on Γ. In particular, a bounded set of eigenvalues can be determined using a space of such polynomial splines with a fixed set of singularities. It is also shown that corresponding eigenfunctions can be reconstructed as uniform limits of the same polynomial splines with appropriate fixed set of singularities. |
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Keywords: | Quantum graphs Polynomial splines Rayleigh– Ritz method Plancherel– Polya inequalities |
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