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Humberto Eduardo Prado Castillo

Full Professor

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

Functional Analysis; Operator Semigroups; Integral Transforms

Mathematics, UNIVERSITY OF IOWA. Estados Unidos, 1989

Instructor Full Time

UNIVERSIDAD DE CHILE

Sciences

Santiago, Chile

1981 - 1983
Assistant Profesor Full Time

OKLAHOMA STATE UNIVERSITY

Stillwater, Estados Unidos

1989 - 1991
Associate Professor Full Time

UNIVERSIDAD CATOLICA DEL NORTE

Sciences

Antofagasta, Chile

1991 - 1995
Full Professor Full Time

UNIVERSIDAD DE SANTIAGO DE CHILE

Sciences

Santiago, Chile

1995 - A la fecha

Full Professor Full Time

Universidad de Santiago de Chile

Santiago, Chile

1995 - A la fecha
Instructor Full Time

Universidad de Chile

Santiago, Chile

1981 - 1983
Assitant Professor Full Time

Oklahoma State University

Oklahoma, Estados Unidos

1989 - 1991
Associate Professor Full Time

Universidad Catolica del Norte

Antofagasta, Chile

1991 - 1995

Master degree thesis

• Juan Márquez, june 2020
• Gabriel Céspedes, august 2017;
• Álvaro Rubilar, july 2016
• Ignacio Olea, September 2014
• José Ramírez, May 2013.
• Cristián Montoya, July 2012.
• Patricio Jara, December 2001
• Luis del Campo Conejeros, June 1995.
• Luis Cortés Vega, September 1994

Ph.D degree thesis:
• José Ramírez, june 2019.
• Mauricio Bravo, may 2015.
• Cecilia Donoso, july 2003.

Humberto Prado

UNIVERSITY OF IOWA

Estados Unidos, 1988

Research assistant


The asymptotic behavior of the time fractional Schrödinger equation on Hilbert space Górka, P. Pons, D., Prado, H. Article WOS JOURNAL OF MATHEMATICAL PHYSICS (2020)
The time fractional Schrödinger equation with a non linearity of Hartree-type Prado, Humberto, Ramírez, José Article SCOPUS, SciSearch JOURNAL OF EVOLUTION EQUATIONS (2020)
A Laplace transform approach to linear equations with infinitely many derivatives and zeta-nonlocal field equations. Article WOS ADVANCES IN THEORETICAL AND MATHEMATICAL PHYSICS (2019)
Nonlinear pseudo-differential equations defined by elliptic symbols on Lp and the fracctional Laplacian Article SCOPUS, WOS ISRAEL JOURNAL OF MATHEMATICS (2019)
The time fractional Schrödinger equation on Hilbert space Article SCOPUS, ISI INTEGRAL EQUATIONS AND OPERATOR THEORY (2017)
Differential Equations with Infinitely Many Derivatives and the Borel Transform Carlsson M.; Prado, H; Reyes E.G. Article ISI SCOPUS ANNALES HENRI POINCARE (2016)
Nonlinear Evolution Equations with Infinitely Many Derivatives Prado, H; Reyes E.G. Article ISI SCOPUS COMPLEX ANALYSIS AND OPERATOR THEORY (2016)
NEW RESULTS FROM OLD INVESTIGATION: A NOTE ON FRACTIONAL m-DIMENSIONAL DIFFERENTIAL OPERATORS. THE FRACTIONAL LAPLACIAN Prado, H; Rivero M.; Velasco, MP Article ISI SCOPUS Fractional Calculus and Applied Analysis (2015)
Parabolic flow on metric measure spaces Gorka, P; Kurek, A; Lazarte, E; Prado, H Article ISI SEMIGROUP FORUM (2014)
Separation dichotomy and wavefronts for a nonlinear convolution equation. Gomez, Carlos; Prado, Humberto; Trofimchuk, Sergei Article JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (2014)
On a General Class of Nonlocal Equations Gorka, P; Prado, H Article ISI SCOPUS ANNALES HENRI POINCARE (2013)
Some results on Laplace-Stieltjes transform Galue, L; Prado, H; Kalla, S Article ISI SCOPUS Kuwait Journal of Science (2013)
The initial value problem for ordinary differential equations with infinitely many derivatives Gorka, P; Prado, H; Reyes E.G. Article ISI SCOPUS Classical and Quantum Gravity (2012)
Nonlinear Equations with Infinitely many Derivatives Gorka, P; Prado, H Article ISI SCOPUS Complex Analysis and Operator Theory (2011)
Completeness in quantum mechanics and the Weyl-Titchmarsh-Kodaira theorem Palma, G; Prado, H Article ISI SCOPUS Journal of Physics A: Mathematical and Theoretical (2010)
Fractional relaxation equations on Banach spaces Lizama, C.; Prado, H Article ISI SCOPUS Applied Mathematics Letters (2010)
Functional calculus via Laplace transform and equations with infinitely many derivatives Gorka, P; Prado, H Article ISI SCOPUS Journal of Mathematical Physics (2010)
On duality and spectral properties of (a, k)-regularized resolvents Lizama, C.; Prado, H Article ISI SCOPUS PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS (2009)
Stability properties for solution operators Prado, H Article ISI SCOPUS SEMIGROUP FORUM (2008)
On the asymptotic behavior of regularized operator farnilies Prado, H Article ISI SCOPUS SEMIGROUP FORUM (2006)
Singular perturbation for Volterra equations of convolution type Lizama, C.; Prado, H Article ISI SCOPUS APPLIED MATHEMATICS AND COMPUTATION (2006)
Singular perturbations of integro-differential equations Lizama, C.; Prado, H Article ISI SCOPUS APPLIED MATHEMATICS AND COMPUTATION (2006)
Resonances for Hamiltonians with a delta perturbation in one dimension Fernández, C.; Palma, G; Prado, H Article ISI SCOPUS JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL (2005)
Rates of approximation and ergodic limits of regularized operator families Lizama, C.; Prado, H Article ISI SCOPUS JOURNAL OF APPROXIMATION THEORY (2003)
Gaussian bounds for reduced heat kernels of subelliptic operators on nilpotent lie groups Ter Elst, AFM; Prado, H Article ISI MATHEMATICA SCANDINAVICA (2002)
Mean Quantum Sojourn Time Accardi L.; Fernández, C.; rebolledo r; Prado, H Article Open Systems and Information Dynamics (1999)
The vector-valued Stieltjes transform Lizama, C.; Prado, H Article QUARTERLY JOURNAL OF MATHEMATICS (1999)
The vector-valued Stieltjes transform Carlos Lizama y Humberto Prado Article QUARTERLY JOURNAL OF MATHEMATICS (1999)
Asymptotic behavior of reduced dynamics on Hilbert sapces Article WOS Quantum Probability Communications (1998)
Large time behavior for discontinuous dynamics on Hilbert spaces Cortes V.H.; Prado, H Article PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY (1997)
Large time behavior of discontinuous dynamics on Hilbert spaces. Cortéz, C. Prado, H. Article WOS Quantum Probability Communications (1997)
Reduced Weil models and representations of Gl(2,R) Article WOS Quantum Probability Communications (1997)
Reduced Weil models for representations of GL(2, ?) and Barnes' lemma Prado H.E. Article JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES (1997)
Sur les temps moyens de séjour quantiques. Prado, Humberto; Accardi, Luigi; Rebolledo, Rolando; Fernández, Claudi Article N/A Quantum Probability Communications (1994)
Reflection positivity for unitary representations of Lie groups. Article N/A Quantum Probability Communications (1992)
A geometric construction of local representations of local Lie groups. Article N/A Quantum Probability Communications (1991)
Spectral properties for operators in a Lie algebra. Article N/A Quantum Probability Communications (1989)
Représentations de GL(2,R) et identités de type Barnes pour la fonction Γ. (French) [Representations of GL(2,R) and Barnes-type identities for the Γ-function] Prado, Humberto Article N/A Quantum Probability Communications (1985)


The Laplace Transform and nonlocal Field Equations Chávez, Alan, Prado Humberto, Reyes Enríque; Mishonor Todor BookSection N/A (2019)
Generalized euclidean bosonic string equations Gorka, Przemyslaw; Prado, Humberto; Reyes, Enrique G.; Benguria R.; Friedman, E; Mantoiu, M. BookSection n/a (2012)
Generalized Euclidean bosonic string equations. Spectral analysis of quantum Hamiltonians Górka, P.; Prado, H.; Reyes, E. G; Benguria, R; Friedman, E; Mantoiu, E BookSection N/A (2012)
Existence of nonnegative solutions for generalized p-Laplacians Prado, H, Ubilla, P.; Caristi, G., Metidieri, E. BookSection N/A Quantum Probability Communications (1998)
Norm estimates for a class of semigroups of Schrödinger type Prado, Humberto; rebolledo r BookSection N/A Quantum Probability Communications (1998)
Integral transform and ordirary differential equations of infinite order BookSection N/A


The Laplace Transform and Nonlocal Field Equations Prado, H; Reyes E.G. ConferencePaper ISI SCOPUS LATIN AMERICAN SCHOOL OF PHYSICS MARCOS MOSHINSKY (ELAF2017) - QUANTUM CORRELATIONS (2019)
On equations with infinitely many derivatives: integral transforms and the Cauchy problem Prado, Humberto; Reyes, Enrique G. ConferencePaper ISI SCOPUS Journal of Physics: Conference Series (2014)
The Laplace Transform in the Study of Equations with Infinitely Many Derivatives Gorka, P; Prado, H ConferencePaper LATIN AMERICAN SCHOOL OF PHYSICS MARCOS MOSHINSKY (ELAF2017) - QUANTUM CORRELATIONS (2010)
Exponential decay for perturbations of pure point hamiltonians Fernández, C.; Prado, H ConferencePaper STOCHASTIC ANALYSIS AND MATHEMATICAL PHYSICS II (2003)


On NonLinear Pseudo Differential Equations=> Equations with Infinitely Many Derivatives and Non Local Equations FONDECYT (1170571) Proyecto 2017-2021 Inv. Principal
On NonLinear Pseudo Differential Equations: Equations with Infinitely Many Derivatives and Non Local Equations Proyecto (2017)
NON CLASSICAL PSEUDO-DIFFERENTIAL EQUATIONS=> FRACTIONAL EVOLUTIONARY EQUATIONS, AND EQUATIONS WITH INFINITELY MANY DERIVATIVES FONDECYT (1130554) Proyecto 2013-2017 Inv. Responsable
THE LONG TIME BEHAVIOR OF SOLUTIONS TO FRACTIONAL EVOLUTION EQUATIONS. FONDECYT (1070127) Proyecto 2007-2011 Inv. Responsable
ON THE ASYMPTOTIC BEHAVIOR OF OPERATOR FAMILIES ASSOCIATED TO LINEAR EVOLUTION EQUATIONS FONDECYT (1030007) Proyecto 2003-2007 Inv. Responsable
A NONCOMMUTATIVE LARGE DEVIATIONS THEORY FONDECYT (3010005) Proyecto 2001-2004 Inv. Patrocinante
MAXIMAL REGULARITY FOR LINEAR EVOLUTIONARY INTEGRAL EQUATIONS IN SPACES OF VECTOR-VALUED FUNCTIONS FONDECYT (1010675) Proyecto 2001-2005 Coinvestigador(a)
SPECTRAL PROPERTIES FOR SUBELLIPTIC AND SUBCOERCIVE OPERATORS ON Lp SPACES FONDECYT (1000811) Proyecto 2000-2003 Inv. Responsable
REGULARIZED SOLUTIONS FOR ABSTRACT VOLETRRA EQUATIONS IN BANACH SPACES FONDECYT (1980812) Proyecto 1998-2001 Coinvestigador(a)
ESTIMACIONES EN NORMA PARA DINAMICAS GENERALIZADAS Y TEORIA ESPECTRAL DE OPERADORES FONDECYT (1970722) Proyecto 1997-2000 Inv. Responsable
EXISTENCIA Y MULTIPLICIDAD DE SOLUCIONES PARA P-LAPLACIANOS GENERALIZADOS Y SISTEMAS HAMILTONIANOS FONDECYT (1950605) Proyecto 1995-1998 Coinvestigador(a)
EXISTENCIA Y MULTIPLICIDAD DE SOLUCIONES PARA P-LAPLACIANOS GENERALIZADOS Y SISTEMAS HAMILTONIANOS FONDECYT (1950605) Proyecto 1995-1998 Coinvestigador(a)
COMPORTAMIENTO ASIMPTOTICO PARA FAMILIAS DE OPERADORES FONDECYT (1930023) Proyecto 1993-1995 Inv. Responsable

Rolando Rebolledo

Full Professor

Universidad de Valparaíso/Facultad de Ingeniería

Valparaíso, Chile

Carlos Lizama

Full Professor

Matematica y Ciencia de la Computación

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

Humberto Prado

Full Professor

Mathemnatics and Computer Sciences

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

Enrique Reyes

Associate Professor

Mathematics and Computer Science

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

Guillermo Palma

Academico Jornada Completa

Departamento de Fisica

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

Humberto Eduardo Prado Castillo

Líneas de Investigación

Educación

Mathematics, UNIVERSITY OF IOWA. Estados Unidos, 1989

Experiencia Académica

Instructor Full Time

Assistant Profesor Full Time

Associate Professor Full Time

Full Professor Full Time

Experiencia Profesional

Full Professor Full Time

Instructor Full Time

Assitant Professor Full Time

Associate Professor Full Time

Formación de Capital Humano

Premios y Distinciones

Humberto Prado

Article (38)

BookSection (6)

ConferencePaper (4)

Proyecto (13)

On NonLinear Pseudo Differential Equations=> Equations with Infinitely Many Derivatives and Non Local Equations

NON CLASSICAL PSEUDO-DIFFERENTIAL EQUATIONS=> FRACTIONAL EVOLUTIONARY EQUATIONS, AND EQUATIONS WITH INFINITELY MANY DERIVATIVES

THE LONG TIME BEHAVIOR OF SOLUTIONS TO FRACTIONAL EVOLUTION EQUATIONS.

ON THE ASYMPTOTIC BEHAVIOR OF OPERATOR FAMILIES ASSOCIATED TO LINEAR EVOLUTION EQUATIONS

A NONCOMMUTATIVE LARGE DEVIATIONS THEORY

MAXIMAL REGULARITY FOR LINEAR EVOLUTIONARY INTEGRAL EQUATIONS IN SPACES OF VECTOR-VALUED FUNCTIONS

SPECTRAL PROPERTIES FOR SUBELLIPTIC AND SUBCOERCIVE OPERATORS ON Lp SPACES

REGULARIZED SOLUTIONS FOR ABSTRACT VOLETRRA EQUATIONS IN BANACH SPACES

ESTIMACIONES EN NORMA PARA DINAMICAS GENERALIZADAS Y TEORIA ESPECTRAL DE OPERADORES

EXISTENCIA Y MULTIPLICIDAD DE SOLUCIONES PARA P-LAPLACIANOS GENERALIZADOS Y SISTEMAS HAMILTONIANOS

EXISTENCIA Y MULTIPLICIDAD DE SOLUCIONES PARA P-LAPLACIANOS GENERALIZADOS Y SISTEMAS HAMILTONIANOS

COMPORTAMIENTO ASIMPTOTICO PARA FAMILIAS DE OPERADORES