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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 (TalEzer),
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
numerical cubature on polygonal elements with curved sides
for the discretization of PDEs, to
computational adaptive
optics
(ray tracing and optical
system design with vignetted annular pupils, e.g. for the the
LSST: LargeSynoptic
Survey Telescope camera), to
regional scale modelling/simulation
in spherical and toroidal
geometry (in particular, geomathematical applications such as
local geomagnetic field modelling).
Software

SUBP (Matlab package for subperiodic trigonometric quadrature and
multivariate applications)
by G. Da Fies, A. Sommariva and M. Vianello
note: contains codes for product Gaussian quadrature on
circular and
spherical sections
Posters
Papers

Lunebased quadrature on vignetted annular pupils
with application to the LSST camera
in preparation  B. Bauman (LLNL, USA), A. Sommariva and M. Vianello

Subperiodic Dubiner distance, norming meshes and trigonometric
polynomial optimization
draft  M. Vianello
Optim. Lett. 12 (2018), 16591667

Discrete
norming inequalities on sections of sphere, ball and torus
preprint  A. Sommariva and M. Vianello
J. Inequal. Spec. Funct. 9 (2018), 113121

Stability inequalities for Lebesgue constants via Markovlike
inequalities
preprint  F. Piazzon and M. Vianello
Dolomites Res. Notes Approx. DRNA 11 (2018), 19

Subperiodic
Trigonometric Hyperinterpolation
preprint  G. Da Fies, A. Sommariva and M. Vianello
in: "Contemporary Computational Mathematics  a celebration of
the 80th birthday
of Ian Sloan" (invited paper)
J. Dick, F.Y.
Kuo, H. Wozniakowski Eds., Springer, 2018, pp. 283304
 Numerical
quadrature on the intersection of planar disks
preprint  A. Sommariva and M. Vianello
FILOMAT 31:13 (2017), 41054115

Subperiodic trigonometric subsampling: a numerical approach
preprint  A. Sommariva and M. Vianello
Appl. Anal. Discrete Math. 11 (2017), 470483
 Polynomial
approximation and quadrature on
geographic rectangles
preprint  M. Gentile, A. Sommariva and M. Vianello
Appl. Math. Comput. 297 (2017), 159179
 Numerical
hyperinterpolation over nonstandard planar
regions
preprint  A. Sommariva and M. Vianello
Math. Comput. Simulation, published online 30 July 2016
 Jacobi norming
meshes
preprint  F. Piazzon and M. Vianello
Math. Inequal. Appl. 19 (2016), 10891095
 Polynomial
fitting and interpolation on
circular sections
preprint  A. Sommariva and M. Vianello
Appl. Math. Comput. 258 (2015), 410424
 Product Gaussian
quadrature on circular
lunes
preprint  G. Da Fies and M. Vianello
Numer. Math. Theory Methods Appl. 7 (2014), 251264

Norming meshes by Bernsteinlike inequalities
preprint  M. Vianello
Math. Inequal. Appl. 17 (2014), 929936

Algebraic cubature by linear blending of
elliptical arcs
preprint  G. Da Fies, A. Sommariva and M. Vianello
Appl. Numer. Math. 74 (2013), 4961

Polynomial
approximation on pyramids, cones and solids of rotation
S. De Marchi and M. Vianello
Dolomites Res. Notes Approx. DRNA 6 (2013), 2026

On the Lebesgue
constant of subperiodic
trigonometric
interpolation
preprint  G. Da Fies and M. Vianello
J. Approx. Theory 167 (2013), 5964

Algebraic cubature on planar lenses and bubbles
G. Da Fies and M. Vianello
Dolomites Res. Notes Approx. DRNA 5 (2012), 712

Trigonometric Gaussian quadrature on subintervals of the
period
preprint  G. Da Fies and M. Vianello
Electron. Trans. Numer. Anal. 39 (2012), 102112

Subperiodic trigonometric interpolation and quadrature
preprint  L. Bos and M. Vianello
Appl. Math. Comput. 218 (2012), 1063010638