Delgado J., Ruzhansky M. (Eds.) Analysis and Partial Differential Equations: Perspectives from Developing Countries, Springer Proceedings in Mathematics & Statistics, Vol. 275, Springer, 2019. xii+269pp link, Doi.
About this book:
This volume presents current trends in analysis and partial differential equations from researchers in developing countries. The fruit of the project 'Analysis in Developing Countries', whose aim was to bring together researchers from around the world, the volume also includes some contributions from researchers from developed countries.
Focusing on topics in analysis related to partial differential equations, this volume contains selected contributions from the activities of the project at Imperial College London, namely the conference on Analysis and Partial Differential Equations held in September 2016 and the subsequent Official Development Assistance Week held in November 2016. Topics represented include Fourier analysis, pseudo-differential operators, integral equations, as well as related topics from numerical analysis and bifurcation theory, and the countries represented range from Burkina Faso and Ghana to Armenia, Kyrgyzstan and Tajikistan, including contributions from Brazil, Colombia and Cuba, as well as India and China.
J. Delgado and M. Ruzhansky. An Introduction to the Weyl-Hörmander Calculus. In Preparation for the series Springer Universitext.
D. Cardona, J. Delgado and M. Ruzhansky. Lp boundedness for pseudo-differential operators on graded Lie groups, Journal of Geometric Analysis. 31, no.12, p. 11603–11647, 2021 Arxiv
J. Delgado and A. Muñoz Tello. On the set of Gateaux differentiability of the L1 norm. to appear in Int. Journal of NonLinear Analysis and Applications.
J. Delgado and A. Muñoz Tello. On the set of Gateaux differentiability of Sobolev norms. In preparation.
D. Cardona, J. Delgado and M. Ruzhansky. Functional calculus on graded Lie groups with applications to diffusion equations. to appear in Journal of Geometric Analysis.
J. Delgado, V. Kumar and M. Ruzhansky. Anharmonic Semigroup and applications to well-posedness for nonlinear PDEs. In preparation
J. Delgado and J. P. Velazquez-Rodriguez. Fundamental solutions of the Vladimirov-Taibleson operator on non-locally Vilenkin groups. Submitted
J. Delgado. On the well-posedness for a class of pseudodifferential diffusion equations on the torus. submitted
M. Chatzakou, J. Delgado and M. Ruzhansky. On a class of anharmonic oscillators II: General case. Submitted
D. Cardona, J. Delgado and M. Ruzhansky. Poincaré determinants on Compact Lie groups. In Preparation.
J. Delgado. A note on the Poincare determinant. To appear in Journal of Pseudodifferential operators and Applications.
D. Cardona, J. Delgado and M. Ruzhansky. Fractional diffusion on compact Lie groups. Submitted
J. Delgado and L. Posada. Nuclearity criteria for power series kernels in higher dimensions. In preparation.
D. Cardona, J. Delgado and M. Ruzhansky. Dixmier traces, Wodzicki residues, and determinants on compact Lie groups. II. In Preparation.
D. Cardona, J. Delgado and M. Ruzhansky. Dixmier traces, Wodzicki residues and determinants on Compact Lie groups. Submitted.
D. Cardona, J. Delgado and M. Ruzhansky. Plemelj-Smithies formulas on Compact Lie groups. to appear in Monatshefte für Mathematik
J. Delgado. On the positivity of the Fourier transform. Submitted.
R. Daher, J. Delgado and M. Ruzhansky Titchmarsh theorems for Fourier transforms of Hölder-Lipschitz functions on compact homogeneous manifolds, Monatsh. Math. 89, no. 1, 23-49 , 2019.
J. Delgado. On the well-posedness of the Cauchy problem for a class of Degenerate parabolic equations , Integral Equations Operator Theory, 90, no. 1, Art. 3, 19 pp., 2018. Open Access
J. Delgado and M. Ruzhansky. Schatten classes and trace formula on compact groups, Mathematical Research Letters, 24, no. 4, 979-1003, 2017. link
J. Delgado and M. Ruzhansky. Fourier multipliers, Symbols and Nuclearity on compact manifolds, Journal d'Analyse Mathématique. 135, no. 2, 757-800, 2018. Open Access
J. Delgado and M. Ruzhansky. Approximation property and nuclearity on variable exponent Lebesgue spaces, Math. Scand., 122, no. 2, 299-319, 2018.
J. Delgado, M. Ruzhansky and N. Tokmagambetov. Schatten classes and Nuclearity of Boundary Value Problems, J. Math. Pures Appl. (9) 107, no. 6, 758783, 2017. Open Access
J. Delgado and M. Ruzhansky Lp bounds for pseudo-differential operators on compact Lie groups, J. Inst. Math. Jussieu, 18, no. 3, 531-559, 2019. Open Access
Delgado J., Ruzhansky M., Fourier multipliers in Hilbert spaces, in Integral Fourier Operators: Proceedings of a Summer School, Ouagadougou 14–25 September 2015 / Sylvie Paycha; Pierre Clavier (eds.). – Potsdam: Universitätsverlag Potsdam, 2018 link
J. Delgado. On the Cauchy problem for a class of Degenerate hyperbolic equations in Weyl-Hörmander calculus. J. Math. Analysis and Applications, 436, No. 1, Pages 339-354, 2016.
J. Delgado, M. Ruzhansky and B. Wang Approximation property and nuclearity on mixed-norm LP , modulation and Wiener amalgam spaces, Journal of London Mathematical Society. 94 (2) : Pages 391408, 2016. Open Access
J. Delgado, M. Ruzhansky and B.Wang Grothendieck-Lidskii trace formula for mixed-norm an variable Lebesgue spaces, J. Spectral. Theory. 6(4) :781-791, 2016
J. Delgado. A class of invertible subelliptic operators in S(m; g)-calculus, Results in Mathematics. 67, No. 33, Pages 431-444, 2015.
J. Delgado and M. Ruzhansky Kernel and symbol criteria for Schatten classes and r-nuclearity on compact manifolds, Comptes Rendus Mathematiques. Ser. I, 352, 779-784, 2014. Open Access
J. Delgado Lp bounds in S(m, g)-calculus, Complex Var. Elliptic Equ. 61, no. 3, Pages 315-337, 2016.
. J. Delgado and M. Ruzhansky. Schatten classes on compact manifolds : Kernel conditions, Journal of Functional Analysis. 267, no. 3, Pages 772-798, 2014. Open Access
J. Delgado On the r-nuclearity of some integral operators on Lebesgue spaces, Tohoku Mathematical Journal. 67, no. 1, Pages 125-135, 2015.
. J. Delgado and M. Ruzhansky Lp-Nuclearity, traces, and Grothendieck-Lidskii formula on compact Lie groups, Journal des Mathématiques Pures et Appliquées. (9) 102, no. 1, 153-172, 2014. Open Access
J. Delgado and M. W. Wong Lp-Nuclear pseudodifferential operators on Z and S1, Proc. Amer. Math. Soc. Volume 141, Number 11, Pages 3935-3942, 2013.
J. Delgado Lp bounds for pseudodifferential operators on the torus, Operator Theory, Advances and Applications, vol. 231, p. 103-116, 2013.
J. Delgado Trace formulas for nuclear operators in spaces of Bochner integrable functions, Monatshefte für Mathematik. Volume 172, Issue 3, Pages 259275, 2013
J. Delgado Sobolev embeddings for a class of pseudodifferential operators. Journal of Pseudo-Differential Operators and Applications. Volume 2, Num 3, p. 399-417 2011.
J. Delgado Lp bounds for a class of fractional powers of subelliptic operators,Pseudo-Differential Operators : Complex Analysis and Partial Differential Equations. Operator Theory, Advances and Applications. Rodino, L, Wong M.W (Eds). vol. 213, p.137-154, 2011.
J. Delgado The trace of nuclear operators on Lp for sigma-finite Borel measure on second countable spaces, Integral Equations and Operator Theory, 68, p. 61-74, 2010.
J. Delgado and Alex M. Zamudio. Invertibility for a Class of Degenerate Elliptic Operators. Journal of Pseudo- Differential Operators and Applications. Vol 1, Num 2 ; p. 207-231, 2010.
J. Delgado A trace for nuclear operators on Lp. Operator Theory, Advances and Applications, vol. 205, p. 181-193, 2009.
J. Delgado Estimations Lp pour une classe d'opérateurs pseudo-differentiels dans le cadre du calcul de Weyl-Hörmander. Journal d'Analyse Mathématique. Vol. 100, p. 337-374, 2006.
SOME PAPERS IN PROGRESS
M. Chatzakou, D. Cardona, J. Delgado and M. Ruzhansky. Lp bounds for a class of Degenerate anharmonic oscillators
Electrical Impedance tomography and singular values
A note on the L2 boundedness of the Cauchy Integral
Regularity for infinitely degenerate elliptic equations