FP7 Operator Ideals

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Marie Curie Project FP7-PEOPLE-2011-IIF Project No 301599

Pseudo-differential operators and operator ideals

Acronym: PseudodiffOperatorS

2012-2014

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Julio Delgado
Julio Delgado

Name of Researcher: Dr Julio DELGADO
Scientist in Charge: Prof Michael Ruzhansky
Imperial College London

PROJECT ABSTRACT

This project is concentrated on the investigation in various independent and intertwined fields in analysis, the theory of pseudo-differential operators, harmonic analysis and the theory of operators ideals. We apply the theory of pseudo-differential operators to study degenerate elliptic equations, degenerate hyperbolic operators, fractional powers of subelliptic operators, Sobolev estimates. In particular we investigate regularity on Sobolev spaces, invertibility and the Cauchy problem for degenerate hyperbolic equations. The study of degenerate equations is a field of intensive research with important applications in physics and engineering. A second field of interest is the study of pseudo-differential operators on compact Lie groups applying techniques of the Weyl-Hormander calculus. Concerning nuclear operators and Schatten-von Neumann ideals we are interested in finding sufficient and/or necessary conditions for the memberships in such kind of ideals, in particular we study different ideals of operators on certain Lie groups and investigate the case of pseudo-differential operators. The study of traces is important in its own, traces of pseudo-differential operators play an essential role in the study of geometric and topological invariants. The membership of a pseudo-differential operator in a Schatten-von Neumann ideal constitutes a way to measure its regularity, and the case of localization operators is relevant in time-frequency analysis.

 PAPERS (written during 2012-2014)

  1. Delgado J., Ruzhansky M., Schatten classes and traces on compact groups, Math. Res. Lett., 24 (2017), 979-1003. arxiv, link
  2. Delgado J., Ruzhansky M., Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds, C. R. Acad. Sci. Paris, Ser. I 352 (2014), 779-784. offprint (open access), arxiv, link
  3. Delgado J., Ruzhansky M., Schatten classes on compact manifolds: Kernel conditions, J. Funct. Anal., 267 (2014), 772-798. offprint (open access), arxiv, link
  4. Delgado J., Ruzhansky M., Fourier multipliers, symbols and nuclearity on compact manifolds, J. Anal. Math., to appear, arxiv
  5. Delgado J., On the r-nuclearity of some integral operators on Lebesgue spaces, Tohoku Math. J., 67 (2015), 125–135. link
  6. Delgado J., A class of invertible subelliptic operators in S(m, g)-calculus, Results Math., 67 (2015), 431–444. link
  7. Delgado J., Lp bounds in S(m,g) calculus, Complex Var. Elliptic Equ., 61 (2016), 315–337. link
  8. Delgado J., Ruzhansky M., Lp-Nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups, J. Math. Pures Appl., 102 (2014), 153-172. offprint (open access), arxiv, link
  9. Delgado J., Trace formulas for nuclear operators in spaces of Bochner integrable functions, Monatshefte fur Mathematik, 172 (2013), 259-275. link
  10. Delgado J., Wong M. W., Lp-nuclear pseudo-differential operators on Z and S1, Proc. Amer. Math. Soc., 141 (2013), 3935-3942.  link

Other joint publications by Julio Delgado and Michael Ruzhansky on arXiv and on MathSciNet