Francis J. Narcowich -- Publications

2011-present

Fuselier, E. and Hangelbroek, T. and Narcowich, F.J. and Ward, J.D. and Wright, G.B., Kernel based quadrature on spheres and other homogeneous spaces. Numerische Mathematik 2013 (online) 1-36. doi: 10.1007/s00211-013-0581-1,

Fuselier, E., Hangelbroek, T., Narcowich, F., Ward, J., and Wright, G. Localized Bases for Kernel Spaces on the Unit Sphere. SIAM Journal on Numerical Analysis 2013 51:5, 2538-2562 doi:10.1137/120876940

T. Hangelbroek, F. J. Narcowich and J. D. Ward, Polyharmonic and Related Kernels on Manifolds: Interpolation and Approximation, Found. Comput. Math., 12 (2012), no. 5, 625-670. doi:10.1007/s10208-011-9113-5.

T. Hangelbroek, W. Madych, F. J. Narcowich and J. D. Ward, Cardinal Interpolation with Gaussian Kernels, J. Fourier Anal. Appl., 18 (2012), no. 1, 67--86. doi:10.1007/s00041-011-9185-2 .

T. Hangelbroek, F. J. Narcowich, X. Sun, and J. D. Ward,Kernel Approximation on Manifolds II: The L-norm of the L2-projector, SIAM J. Math. Anal., 43 (2011), no. 2, 662--684.

2006-2010

T. Hangelbroek, F. J. Narcowich and J. D. Ward, Kernel Approximation on Manifolds I. Bounding the Lebesgue Constant, SIAM J. Math. Anal., 42 (2010) 1732-1760.

F. J. Narcowich, X. Sun, J. D. Ward and Z. Wu, LeVeque type inequalities and discrepancy estimates for minimal energy configurations on spheres, J. Approx. Theory, 162 (2010), 1256-1278.

H. N. Mhaskar, F. J. Narcowich, J. Prestin and J. D. Ward, Lp Bernstein estimates and approximation by spherical basis functions, Math. Comp., 79 (2010), 1647-1679.

E. J. Fuselier, F. J. Narcowich, J. D. Ward, and G. B. Wright, Error and Stability Estimates for Surface-Divergence Free RBF Interpolants on the Sphere, Math. Comp., 78 (2009), 2157-2186.

Albert Boggess and Francis J. Narcowich, A First Course in Wavelets with Fourier Analysis, Second Edition, John Wiley & Sons, Hoboken, NJ, 2009. ISBN 978-0-470-43117-7.

F. J. Narcowich, J. D. Ward, and G. B. Wright, Divergence-free RBFs on Surfaces, J. Fourier Anal. Appl., 13 (2007), 643-663.

F. J. Narcowich, X. Sun, J. D. Ward, and H. Wendland, Direct and Inverse Sobolev Error Estimates for Scattered-Data Interpolation via Spherical Basis Functions, Found. Comput. Math., 7 (2007), 369-390.

F. J. Narcowich, X. Sun, and J. D. Ward, Approximation Power of RBFs and Their Associated SBFs: A Connection, Adv. Comput. Math., 27 (2007), 107-124.

F. J. Narcowich, P. Petrushev, and J. D. Ward, Decomposition of Besov and Triebel-Lizorkin spaces on the sphere, J. Funct. Anal., 238 (2006), 530-564.

F. J. Narcowich, P. Petrushev, and J. D. Ward, Localized Tight Frames on Spheres, SIAM J. Math. Anal., 38 (2006), 574-594.

Q. T. Le Gia, F. J. Narcowich, J. D. Ward, and H. Wendland, Continuous and Discrete Least-Squares Approximation by Radial Basis Functions on Spheres, J. Approx. Theory, 143 (2006), 124-133.

F. J. Narcowich, J. D. Ward, and H. Wendland, Sololev Error Estimates and a Bernstein Inequality for Scattered-Data Interpolation via Radial Basis Functions, Constr. Approx., 24 (2006) 175-186. DOI 10.1007/s00365-005-0624-7, URL http://dx.doi.org/10.1007/s00365-005-0624-7.

2001-2005

F. J. Narcowich, Recent Developments in Error Estimates for Scattered-Data Interpolation via Radial Basis Functions, Numer. Algorithms, 39 (2005), 307-315.

F. J. Narcowich, J. D. Ward, and H. Wendland, Sololev Bounds on Functions with Scattered Zeros, with Applications to Radial Basis Function Surface Fitting, Math. Comp., 74 (2005), 743-763.

F. J. Narcowich and J. D. Ward, Scattered-Data Interpolation on Rn: Error Estimates for Radial Basis and Band-limited Functions, SIAM J. Math. Anal., 36 (2004), 284-300.

F. J. Narcowich, J. D. Ward, Preface [Computation and approximation on the sphere], Adv. Comput. Math. 21 (2004), no. 1-2, 1--2.

H. N. Mhaskar, F.J. Narcowich and J. D. Ward, On the representation of band-dominant functions on the sphere using finitely many bits, Adv. Comput. Math., 21 (2004), 127-146.

F. J. Narcowich, J. D. Ward, and H. Wendland, Refined Error Estimates for Radial Basis Function Interpolation, Constr. Approx., 19 (2003), 541-564.

H. N. Mhaskar, F. J. Narcowich, and J. D. Ward, Zonal function network frames on the sphere, Neural Networks, 16 (2003) 183-203.

R. A. Lorentz, F. J. Narcowich, and J. D. Ward, Collocation Discretizations of the Transport Equation with Radial Basis Functions, Appl. Math. Comput., 145 (2003), 97-116.

F. J. Narcowich and J. D. Ward, Scattered-Data interpolation on the Sphere: Error Estimates and Locally Supported Basis Functions, SIAM J. Math. Anal., 33 (2002), 1393-1410.

F. J. Narcowich, N. Sivakumar, and J. D. Ward, On convergent interpolatory processes associated with periodic-basis functions, Acta Sci. Math. (Szeged), 68 (2002), 133-161.

H. N. Mhaskar, F. J. Narcowich, N. Sivakumar, and J. D. Ward, Approximation with Interpolatory Constraints, Proc. Amer. Math. Soc., 130 (2002), 1355-1364.

F. J. Narcowich, R. Schaback, and J. D. Ward, Approximation in Sobolev spaces by kernel expansions, J. Approx. Theory, 114 (2002) 70-83.

Albert Boggess and Francis J. Narcowich, A First Course in Wavelets with Fourier Analysis, Prentice-Hall, Upper Saddle River, NJ, 2001. ISBN 0-13-022809-5.

H. N. Mhaskar, F. J. Narcowich, and J. D. Ward, ``Representing and Analyzing Scattered Data on Spheres,'' Multivariate Approximation and Applications, edited by N. Dyn, D. Leviatan, D. Levin, and A. Pinkus, Cambridge University Press, Cambridge, U. K., 2001.

H. N. Mhaskar, F. J. Narcowich, and J. D. Ward, Spherical Marcinkiewicz-Zygmund Inequalities and Positive Quadrature, Math. Comp., 70 (2001) 1113-1130.

1996-2000

H. N. Mhaskar, F. J. Narcowich, and J. D. Ward, Neural network frames on the sphere; in ``Neural networks for signal processing, X, (B. Widrow, L. Guan, K. Paliwa, T. Adall, J. Larsen, E. Wilson, and S. Douglas Eds.), IEEE, New York, 2000, pp. 175--184.

H. N. Mhaskar, F. J. Narcowich, J. Prestin, and J. D. Ward, Polynomial frames on the sphere, Adv. Compt. Math., 13 (2000), 387-403.

H. N. Mhaskar, F. J. Narcowich, and J. D. Ward, Quasi-interpolation in shift invariant spaces, J. Math. Anal. Appl., 251 (2000) 356-363.

T. H. O'Donnell, F. J. Narcowich, H.L. Southall, and J. D. Ward, ``Multiple source direction finding with reduced training and increased generalization,'' in proceedings of the Millenium Conference on Antennas and Propagation, 9 - 14 April 2000, Davos, Switzerland; ESA publication SP-444.

H. N. Mhaskar, F. J. Narcowich, and J. D. Ward, Approximation Properties of Zonal Function Networks Using Scattered Data on the Sphere, Adv. Comput. Math., 11 (1999) 121-137.

F. J. Narcowich, R. Schaback, and J. D. Ward, Multilevel Interpolation and Approximation, Appl. Comput. Harmonic Anal., 7 (1999) 243-261.

N. Dyn, F.J. Narcowich and J.D. Ward, Variational Principles and Sobolev-Type Estimates for Generalized Interpolation on a Riemannian Manifold, Constr. Approx., 15 (1999) 175-208.

F. J. Narcowich, N. Sivakumar, and J. D. Ward, Stability Results for Scattered-Data Interpolation on Euclidean Spheres, Adv. Comp. Math., 8 (1998) 137-163.

F. J. Narcowich, Recent Developments in Approximation via Positive Definite Functions, in Approximation Theory IX, Volume 2: Computational Aspects, C. K. Chui and L. Schumaker (eds.), Vanderbilt University Press, Nashville, TN, 1998, pp. 221-242.

N. Dyn, F.J. Narcowich and J. D. Ward, A Framework for Interpolation and Approximation on a Riemannian Manifold, Approximation Theory and Optimization: Tributes to M. J. D. Powell ed. by M. D. Buhman and A. Iserles, Cambridge University Press, Cambridge, U. K., 1997.

F.J. Narcowich and J.D. Ward, Nonstationary wavelets on the m-sphere for scattered data Appl. Comput. Harmonic Anal., 3, (1996) 324-336.

F.J. Narcowich and J.D. Ward, Wavelets associated periodic basis functions, Appl. Comput. Harmonic Anal., 3, (1996) 40-56.

1991-1995

F. J. Narcowich and J. D. Ward, Nonstationary Spherical Wavelets for Scattered Data, in Approximation Theory VIII, vol. 2: Wavelets and Multilevel Approximation, pp. 301-308, Charles K. Chui and Larry L. Schumaker, eds., World Scientific, Singapore, 1995.

F. J. Narcowich, P. W. Smith, and J. D. Ward, Density of Translates of Radial Functions on Compact Sets, in Approximation Theory VIII, vol. 2: Wavelets and Multilevel Approximation, pp. 301-308, Charles K. Chui and Larry L. Schumaker, eds., World Scientific, Singapore, 1995.

F.J. Narcowich, Generalized Hermite Interpolation and Positive Definite Kernels on a Riemannian Manifold, J. Math. Anal. Appl., 190 (1995), 165-193.

A. J. Kurdila, F. J. Narcowich, and J. D. Ward, Persistency of Excitation in Identification Using Radial Basis Approximants," SIAM J. Control and Optimization, 33 (1995), 625-642.

F.J. Narcowich, Grid-free methods of Hermite interpolation with RBF-like functions on a manifolds, pgs. 367-369 in Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, I, held at Georgia Tech on 11-15 July, 1994, ed. by W. F. Ames, IMACS, New Jersey, 1994.

F.J. Narcowich and J.D. Ward, Generalized Hermite Interpolation via Matrix-Valued Conditonally Positive Definite Functions, Math. Comp., 63 (1994), 661-688.

F. J. Narcowich, N. Sivakumar, and J. D. Ward, On Condition Numbers Associated With Radial-Function Interpolation. J. Math. Anal. Appl., 186 (1994), 457-485.

A. J. Kurdila and F.J. Narcowich, Sufficient conditions for penalty formulation methods in analytical dynamics, Computational Mechanics, 12 (1993), 81-96.

F. J. Narcowich, N. Sivakumar, and J. D. Ward, ``Estimates on Condition Numbers for Interpolation Matrices Associated with certain Order 0 Radial Functions,'' in Advances in Computer Methods for Partial Differential Equations VII, R. Vichnevetsky, D. Knight, and G. Richter (eds.), IMACS, New Jersey, 1992.

F.J. Narcowich and J.D. Ward, Norm Estimates for the Inverses of a General Class of Scattered-Data Radial-Function Interpolation Matrices, J. Approx. Theory, 69 (1992), 84-109.

F. J. Narcowich and J. D. Ward, Norms of Inverses for Matrices Associated with Scattered Data, pp. 341-348 in Curves and Surfaces, ed. by P.-J. Laurent, A. Le Mehaute, and L. L. Schumaker, Academic Press, Inc., San Diego, CA, 1991.

A. J. Kurdila, J. L. Junkins, L. Kealey, F. J. Narcowich, and M. Bakich, Approximation of Poincaré Sections Arising in Attitude Control, pp. 1721-1735 in Astrodynamics 1991, Part III, ed. by B. Kaufman et al., Univelt, San Diego, CA, 1992.

F. J. Narcowich and J. D. Ward, Norms of inverses and condition numbers for matrices associated with scattered data, J. Approx. Theory, 64 (1991), 69-94.

G. Chen, S. A. Fulling, F. J. Narcowich, and S. Sun, Exponential decay of energy of evolution equations with locally distributed damping, SIAM J. Appl. Math. 51 (1991), 266-301.

1986-1990

G. Chen, S.A. Fulling, F.J. Narcowich, C. Qi, An asymptotic average decay rate for the wave equation with variable coefficient viscous damping, SIAM J. Appl. Math., 50 (1990), 1341-1347.

F.J. Narcowich, Geometry and Uncertainty, J. Math. Phys., 31 (1990), 354-364.

F.J. Narcowich, Distributions of hbar-Positive Type and Applications, J. Math. Phys., 30 (1989), 2565-2573.

F.J. Narcowich, Conditions for the Convolution of two Wigner distributions to be itself a Wigner distribution, J. Math. Phys. 29 (1988), 2036-2041.

F.J. Narcowich and R.F. O'Connell, A unified approach to quantum dynamical maps and Gaussian Wigner functions, Phys. Lett. A, 133 (1988), 167-170.

F. J. Narcowich, ``A Quantum Mechanical Moment Problem'', Proceedings of the First International Conference on the Physics of Phase Space, held at College Park, Md, 20-23 May 1986, Springer Lecture Notes in Physics 278, ed. by Y.S. Kim and W.W. Zachary, Springer-Verlag, Berlin, 1987.

F.J. Narcowich, The Problem of Moments in the Phase Space Formulation of Quantum Mechanics, J. Math. Phys., 28 (1987), 2873-2882.

F.J. Narcowich and R.F. O'Connell, Necessary and sufficient conditions for a phase-space function to be a Wigner distribution, Phys. Rev. A, 34 (1986), 1-6.

F.J. Narcowich, A Dyson-like expansion for solutions to the quantum Liouville equation, J. Math. Phys., 27 (1986), 2502-2510.

1981-1985

F.J. Narcowich, On the Quantum Liouville Equation, Physica. 134A (1985) 193-208.

F.J. Narcowich, J.D. Ward, and D. Legg, Best Approximation from Stepped Subspaces, Journal of Approximation Theory and its Applications, 1 (1985), 29-49.

F.J. Narcowich and J.D. Ward, Toeplitz-Hausdorff Systems, Linear Algebra Appl., 62 (1984), 183-193.

F.J. Narcowich and J.D. Ward, A Characterization of Essential Matrix Ranges, Bull. London Math. Soc. 14 (1982) 107-111.

F.J.Narcowich and J.D. Ward, Support Functions for Matrix Ranges: Analogues of Lumer's Formula, J. Operator Th., 7(1982), 25-49.

S.A. Fulling and F.J. Narcowich, A basis for local solutions of an elliptic operator, J. Math. Anal. Appl, 86 (1982) 246-267.

F.J. Narcowich and J.D. Ward, A Toplitz-Hausdorff Theorem for Matrix Ranges, J. Operator Th., 6 (1981) 87-101.

S. A. Fulling, F. J. Narcowich, and R. M. Wald, Singularity structure of the two-point function in quantum field theory in curved space-time. II, Ann. Phys. (NY) 136 (1981), 243-272.

1976-1980

F.J. Narcowich, Analytic Properties of the boundary of the Numerical Range, Indiana U. Math. J., 29 (1980), 67-77.

S. Barone, F.J. Narcowich, M.A. Narcowich, Flouquet Theory and Applications, Phys. Review A, 15 (1977) 1109-1125.

F.J. Narcowich, On the Extreme Points of the Interval Between Two Operator, Proc. of AMS, 67 (1977) 84-87.

F.J. Narcowich, R-Operators, II. On the Approximation of Certain Operator-Valued Analytic Functions and the Hermitian Moment Problem, Indiana U. Math. J., 26 (1977) 483-513.

F.J. Narcowich, An Imbedding Theorem for Indeterminate Hermitian Moment Sequences, Pac. J. of Math., 66 (1976), 499-507.

G.D. Allen and F.J. Narcowich, R-Operators, I. Representation Theory and Applications, Indiana Univ. Math. Journal, 25 (1976) 945-963.

1974-1975

G. D. Allen and F. J. Narcowich, On the Representation and Appproximation of the Class of Operator-Valued Analytic Functions, Bull. Amer. Math. Soc., 81 (1975) 440-442.

G.D. Allen, F.J. Narcowich, and J. Williams, An Operator Version of a Theorem of Kolmogorov, Pac. J. Math., 61 (1975) 305-311.

G.D. Allen and F.J. Narcowich, Convergence of the Diagonal Operator-Valued Padé Approximants to the Dyson Expansion, Comm. Math. Phys., 45 (1975) 153-157.

G.D. Allen, C.K. Chui, W.R. Madych, F.J. Narcowich and P.W. Smith, ``Pade Approximation and Orthogonal Polynomials'', Bull. of the Australian Math. Soc., 10 (1974), 263-270.

G.D. Allen, C.K. Chui, W.R. Madych, F.J. Narcowich and P.D. Smith, ``Pade Approximation and Guassian Quadrature'', Bull. of the Australian Math. Soc., 11 (1974) 63-69.

G.D. Allen, C.K. Chui, W.R. Madych, F.J. Narcowich and P.W. Smith, ``Pade Appoximation of Stieltjes Series'', J. Approx. Theory, 14 (1974) 302-316.

F.J. Narcowich, Mathematical Theory of the R-Matrix, I. The Eigenvalue Problem, J. Math. Phys., 15 (1974), 1626-1634.

F.J. Narcowich, Mathematical Theory of the R-Matrix, II. The R-Matrix and its Properties, J. Math. Phys. 15 (1974), 1635-1642.