Spectral characteristics of multiplication, differentiation and integration operators in the generalized Hermite basis
Mathematics. Physics. Mechanics
Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia
AbstractIn this paper generalized Hermite functions are considered, recurrent expressions of its derivatives and primitives are obtained. Calculating algorithms of spectral characteristics for multiplication, differentiation, and integration operators are formulated. They are approved on a number of examples (including functional approximation, approximation of derivatives and primitives, analysis of linear deterministic control systems).
Keywords:basis, Hermite polynomials; Hermite functions; spectral method; spectral characteristic