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SPHA: SubPeriodic Harmonic Analyis


SubPeriodic Harmonic Analysis concerns trigonometric approximation on subintervals of the period. It is connected to the theory of Fourier Extensions (Boyd, Huybrechs, Adcock, et al.), to the recent theory of nonperiodic trigonometric approximations (Tal-Ezer), and to multivariate approximation and cubature on regions defined by circular arcs, such as planar circular sections and surface/solid sections of sphere, cylinder and torus (for example sectors, lenses, lunes, quadrangles, collars, slices, caps). There are several potential multivariate applications, for example to computational optics (ray tracing and optical system design), or to modelling/simulation in spherical and toroidal geometry (in particular, geomathematical applications such as geomagnetic field modelling at regional scales).

Software

Posters

Papers

  1. Discrete norming inequalities on sections of sphere, ball and torus
    draft - A. Sommariva and M. Vianello
  2. Stability inequalities for Lebesgue constants via Markov-like inequalities
    draft - F. Piazzon and M. Vianello
  3. Subperiodic Trigonometric Hyperinterpolation
    draft - G. Da Fies, A. Sommariva and M. Vianello
    to appear in: "Festschrift for the 80th Birthday of Ian Sloan" (invited paper), J. Dick, F.Y. Kuo, H. Wozniakowski Eds., Springer, 2018
  4. Subperiodic trigonometric subsampling: a numerical approach
    draft - A. Sommariva and M. Vianello
    Appl. Anal. Discrete Math., to appear
  5. Numerical quadrature on the intersection of planar disks
    preprint - A. Sommariva and M. Vianello
    FILOMAT 31:13 (2017)
  6. Polynomial approximation and quadrature on geographic rectangles
    preprint - M. Gentile, A. Sommariva and M. Vianello
    Appl. Math. Comput. 297 (2017), 159--179
  7. Numerical hyperinterpolation over nonstandard planar regions
    preprint - A. Sommariva and M. Vianello
    Math. Comput. Simulation, published online 30 July 2016
  8. Jacobi norming meshes
    preprint - F. Piazzon and M. Vianello
    Math. Inequal. Appl. 19 (2016), 1089--1095
  9. Polynomial fitting and interpolation on circular sections
    preprint - A. Sommariva and M. Vianello
    Appl. Math. Comput. 258 (2015), 410--424
  10. Product Gaussian quadrature on circular lunes
    preprint - G. Da Fies and M. Vianello
    Numer. Math. Theory Methods Appl. 7 (2014), 251--264
  11. Norming meshes by Bernstein-like inequalities
    preprint - M. Vianello
    Math. Inequal. Appl. 17 (2014), 929--936
  12. Algebraic cubature by linear blending of elliptical arcs
    preprint - G. Da Fies, A. Sommariva and M. Vianello
    Appl. Numer. Math. 74 (2013), 49--61
  13. Polynomial approximation on pyramids, cones and solids of rotation
    S. De Marchi and M. Vianello
    Dolomites Res. Notes Approx. DRNA 6 (2013), 20--26
  14. On the Lebesgue constant of subperiodic trigonometric interpolation
    preprint - G. Da Fies and M. Vianello
    J. Approx. Theory 167 (2013), 59--64
  15. Algebraic cubature on planar lenses and bubbles
    G. Da Fies and M. Vianello
    Dolomites Res. Notes Approx. DRNA 5 (2012), 7--12
  16. Trigonometric Gaussian quadrature on subintervals of the period
    preprint - G. Da Fies and M. Vianello
    Electron. Trans. Numer. Anal. 39 (2012), 102--112
  17. Subperiodic trigonometric interpolation and quadrature
    preprint - L. Bos and M. Vianello
    Appl. Math. Comput. 218 (2012), 10630--10638