On Generalized Gaussian Quadratures for Exponentials and Their Applications

Beylkin, 1995, On the fast Fourier transform of functions with singularities, Appl. Comput. Harmon. Anal., 2, 363, 10.1006/acha.1995.1026 Cassels, 1956, On the sums of powers of complex numbers, Acta Math. Acad. Sci. Hungar., 7, 283, 10.1007/BF02020524 Cheng, 1999, A fast adaptive multipole algorithm in three dimensions, J. Comput. Phys., 155, 468, 10.1006/jcph.1999.6355 Delsarte, 1984, Spectral properties of finite Toeplitz matrices Dutt, 1993, Fast Fourier transforms for nonequispaced data, SIAM J. Sci. Comput., 14, 1368, 10.1137/0914081 Gohberg, 1992, Circulants, displacements and decompositions of matrices, Integral Equations Operator Theory, 15, 730, 10.1007/BF01200697 Gohberg, 1972, The inversion of finite Toeplitz matrices and their continual analogues, Mat. Issled., 7, 201 Grenander, 1984 Heinig, 1984 Horn, 1994 Jones, 1989, Moment theory, orthogonal polynomials, quadrature, and continued fractions associated with the unit circle, Bull. London Math. Soc., 21, 113, 10.1112/blms/21.2.113 Karlin, 1966, XV Kreı̆n, 1977, 50 Landau, 1965, The eigenvalue behavior of certain convolution equations, Trans. Amer. Math. Soc., 115, 242, 10.1090/S0002-9947-1965-0199745-4 Landau, 1961, Prolate spheroidal wave functions, Fourier analysis and uncertainty II, Bell System Tech. J., 40, 65, 10.1002/j.1538-7305.1961.tb03977.x Lu, 1994, Fast solution of confluent Vandermonde linear systems, SIAM J. Matrix Anal. Appl., 15, 1277, 10.1137/S089547989324416X Markov, 1898, On the limiting values of integrals in connection with interpolation, Zap. Imp. Akad. Nauk. Fiz.-Mat. Otd., 8 Markov, 1948 Montgomery, 1994 Pisarenko, 1973, The retrieval of harmonics from a covariance function, Geophys. J. R. Astr. Soc., 33, 347, 10.1111/j.1365-246X.1973.tb03424.x Rost, 1998, Inversion formulas and fast algorithms for Löwner–Vandermonde matrices Schoenberg, 1973, 12 Slepian, 1978, Prolate spheroidal wave functions, Fourier analysis and uncertainty V. The discrete case, Bell System Tech. J., 57, 1371, 10.1002/j.1538-7305.1978.tb02104.x Slepian, 1961, Prolate spheroidal wave functions, Fourier analysis and uncertainty I, Bell System Tech. J., 40, 43, 10.1002/j.1538-7305.1961.tb03976.x Slepian, 1965, Some asymptotic expansions for prolate spheroidal wave functions, J. Math. Phys., 44, 99, 10.1002/sapm196544199 Szegö, 1975 Trench, 1994, Some spectral properties of Hermitian Toeplitz matrices, SIAM J. Matrix Anal. Appl., 15, 938, 10.1137/S0895479892239007 Turán, 1984 Xiao, 2001, Prolate spheroidal wavefunctions, quadrature and interpolation, Inverse Problems, 17, 805, 10.1088/0266-5611/17/4/315 Yarvin, 1999, Generalized Gaussian quadratures and singular value decompositions of integral operators, SIAM J. Sci. Comput., 20, 699, 10.1137/S1064827596310779 Yarvin, 1999, An improved fast multipole algorithm for potential fields on the line, SIAM J. Numer. Anal., 36, 629, 10.1137/S0036142997329232