document: On generalized Gaussian quadratures for exponentials and their applications We introduce new families of Gaussian-type quadratures for weighted integrals of exponential functions and consider their applications to integration and interpolation of bandlimited functions . We use a generalization of a representation theorem due to Caratheodory to derive these quadratures . For each positive measure , the quadratures are parameterized by eigenvalues of the Toeplitz matrix constructed from the trigonometric moments of the measure . For a given accuracy epsilon , selecting an eigenvalue close to epsilon yields an approximate quadrature with that accuracy . To compute its weights and nodes , we present a new fast algorithm . These new quadratures can be used to approximate and integrate bandlimited functions , such as prolate spheroidal wave functions , and essentially bandlimited functions , such as Bessel functions . We also develop , for a given precision , an interpolating basis for bandlimited functions on an interval
doc_bio_tags: O B I I O O O O O O O O O O O O O B I O B I O O O O O B O B O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B I O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I I I O O O B I O O O B I O O O O O O O O O O O O O O B I O O O
extractive_keyphrases: generalized gaussian quadratures weighted integrals exponential functions integration interpolation bandlimited functions eigenvalues toeplitz matrix trigonometric moments prolate spheroidal wave functions bessel functions
abstractive_keyphrases: caratheodory representation theorem approximation