I had published papers on differential equations in Banach spaces; on interpolation, approximation, and embedding theorems for Sobolev and Besov functions on manifolds. In particular, I started analysis of traces of functions which are smooth with respect to nonholonomic vector fields. I initiated development of the so-called Shannon sampling and variational splines on compact and non-compact Riemannian and sub-Riemannian manifolds and applied them to Radon transform on manifolds; constructed Parseval localized frames (wavelets) on manifolds with applications to CMB. My development of Shannon sampling and splines on combinatorial and quantum graphs became one of the starting points of what is known as the Graph Signal Processing.

Recent Publications

  1. Pesenson, Isaac Z., Splines and Wavelets on Geophysically Relevant Manifolds. Handbook of Geomathematics, 1-32, Springer-Verlag London 2014.
  2. C.Durastanti, Y.Fantaye, F.Hansen, D.Marinucci, I.Pesenson, Simple proposal for radial 3D needlets. Phys. Rev. D 90, 103532 Published 26 November 2014
  3. Fuhr, Hartmut; Pesenson, Isaac Z., Poincare and Plancherel-Polya inequalities in harmonic analysis on weighted combinatorial graphs. SIAM J. Discrete Math. 27 (2013), no. 4, 2007-2028.
  4. Bernstein, Swanhild; Pesenson, Isaac Z., The Radon transform on SO(3): motivations, generalizations, discretization. Geometric analysis and integral geometry, 77-96, Contemp. Math., 598, Amer. Math. Soc., Providence, RI, 2013.