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Taylor series for the dirac function on perturbed surfaces with applications to mechanics
Author(s) -
Codaccioni R. Caboz J.P.,
Constantinescu F.,
Meister E.
Publication year - 1985
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670070128
Subject(s) - mathematics , hamiltonian (control theory) , taylor series , perturbation (astronomy) , hamiltonian system , mathematical physics , mathematical analysis , dirac delta function , lagrangian , analytic function , classical mechanics , quantum mechanics , physics , mathematical optimization
Let H 0 be the Hamiltonian of an unperturbed oscillating system and let V be a small perturbation which is analytic in a neighborhood of the surface H 0 = E, E > 0. If H 0 = H + λ V is the total Hamiltonian, we prove that there is a Taylor expansion of the Dirac function δ for small |λ|When applied to test functions which are analytic near H 0 = E . The connection of this result with the classical Lagrange‐Bürmann theorem and some applications to the mechanics of non‐linear systems are discussed.