Thesis Advisor

Undergraduate Level:

C. Molina, Caos en sistemas lineales de dimension infinita. Universidad de Santiago de Chile, 2022.

J. Arevalo, Regularidad maximal para ecuaciones en diferencias de orden fraccionario. Universidad de Santiago de Chile, 2019.

L. Zuniga, Energy decay in the Moore-Gibson-Thompson equation with frictional damping, (spanish), Universidad de Santiago de Chile, 2016.

J. Pereira, Exponential stability for systems of differential equations in time scales with applications to a model in economy, (spanish), Universidad de Santiago de Chile, 2016.

R. Nuñez, Stability for (a,k)-regularized families of linear operators, (spanish), University of Santiago de Chile, 2014.

R. Brevis, Fractional Fourier Transform in Magnetic Resonance Imaging, (spanish), University of Santiago de Chile, 2011.

B. Galaz, Introduction to Abstract Analysis, (spanish), University of Santiago de Chile, 2008.

E. Coronado, Functions in several variables, an introduction, (spanish), University of Santiago de Chile, 2008.
C. Fernandez, Laplace transform and Volterra equations, (spanish),University of Santiago de Chile, 2006.
R. Ponce, An introduction toWavelets, (spanish), University of Santiagode Chile, 2006.
D. Araya, S. Calzadillas, Fredholm's integral equations. An introduction. (spanish), University of Santiago de Chile, 2005.
M. Guerrero, An introduction to the theory of strongly continuous cosinefamilies of operators (spanish), University of Santiago de Chile, 2004.
H. Andrades, An introduction to the theory of C0-semigroups. (spanish), University of Santiago de Chile, 2003.
K. Matamala, Spectral theory in the study of diffeerential equations (spanish), University of Santiago de Chile, 1999.
A. Garrido, The convolution transform, an introduction (spanish), University of Santiago de Chile, 1999.
J. Avila, Applications of harmonic analysis to partial differential equations (spanish), University of Santiago de Chile, 1994.
A. Meza, A study of C*- algebras with applications to semigroup theory (spanish), University of Santiago de Chile, 1993.
G. Touma, Applications of some theorems in Complex Analysis to evolution equations (spanish), University of Santiago de Chile, 1993.

Graduate Level:
M.Sc. Thesis

J. Bravo, Methods of operator theory for fractional difference equations (spanish), M.Sc. Mathematics, USACH, 2018.

C. Leal, Existence of strong solutions for a class of semilinear evolution equations with non-local initial conditions (spanish), M.Sc. Mathematics, USACH, 2013.

S. Calzadillas, Bounded and mild solutions for Volterra equations (spanish), M.Sc. Mathematics, USACH, 2010.

D. Araya, Almost automorphic solutions for differential and difference equations (spanish), M.Sc. Mathematics, USACH, 2010.

V. Poblete, On multiplicative perturbation for resolvent families of operators (spanish), M. Sc. Mathematics, USACH, 2002.

V. Vergara, Conditions for the uniform stability for resolvent families of operators (spanish), M. Sc. Mathematics, USACH, 2001.

Ph.D. Thesis

J. Miron Aquino, Ph.D. Mathematics, Universidade Estadual Paulista and USACH, Brasil and Chile, under development.

J. Bravo, Existence and qualitative properties of solutions for abstract problems with nonlocal operators. Ph.D. Mathematics at Universidad de Santiago de Chile, 2023.

S. Diaz, Well-posedness and qualitative properties for abstract time-difference equations. Ph.D. Mathematics at Universidad del Norte, Barranquilla, Colombia, 2021

S. Rueda, Qualitative properties for abstract evolution equations in continuous and discrete time. Ph.D. Mathematics, Universidad de Santiago de Chile, 2021.

J. González-Camus, New challenges in Volterra equations and the discrete fractional Laplacian. Ph.D. Mathematics, Universidad de Santiago de Chile, 2020.

L. R. Gambera, Zero-one law for (a,k)-regularized resolvent families and the Blackstock-Crighton-Westervelt equation on Banach spaces. Ph.D. Mathematics, Universidade Estadual Paulista and USACH, Brasil and Chile, 2020.

C. Leal, On qualitative properties of fractional-difference equations on abstract spaces and their applications to lattices models, Ph.D. Mathematics, University of Santiago de Chile, 2018.

A. Pereira, Qualitative properties of resolvent families of operators, Ph.D. Mathematics, University of Talca, 2017.

J.C. Pozo, Regularity and qualitative properties for solutions of some evolution equations, Ph.D. Mathematics, University of Chile, 2013.

F. Poblete, (a,k)-regularized families and some evolution equations,  Ph.D. Mathematics, University of Chile, 2013.

R.Ponce, Bounded solutions to evolution equations in Banach spaces, Ph.D. Mathematics, University of Santiago de Chile, 2011.

J.C. De Souza, A regularity theory for evolution equations in discrete and continuous time, Ph.D. Mathematics, University of Pernambuco, Brazil, 2009.

V. Poblete, Fourier multipliers and maximal regularity for integrodifferential equations in Banach spaces, Ph.D. Mathematics, University of Santiago de Chile, 2006.

Posdoctoral Positions Supervised

S. Zamorano, January - June 2017- March 2021; Ph.D. Universidad de Chile, Chile.

L. Abadías, April 2016- December 2016; Ph.D. Universidad de Zaragoza, Spain.

M.P. Velasco, March 2015-June 2015; Ph.D. Universidad Complutense de Madrid, Spain.

J. G.Mesquita, Nov. 2012-April 2013; Ph.D. University of Sao Paulo, Brazil.

E. Alvarez, Nov.2011-Dec.2011; Ph.D. University of Puerto Rico, USA.

V. Poblete, April 2007- Sept. 2008; Ph.D. University of Santiago, Chile.

V. Vergara, April 2007- Sept. 2008; Ph.D. University of Halle, Germany.

Last Update:  December 2023