Man

Humberto Eduardo Prado Castillo

Full Professor

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

Líneas de Investigación


Functional Analysis; Operator Semigroups; Integral Transforms

Educación

  •  Mathematics, UNIVERSITY OF IOWA. Estados Unidos, 1989

Experiencia Académica

  •   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

Experiencia Profesional

  •   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

Formación de Capital Humano


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.


Premios y Distinciones

  •   Humberto Prado

    UNIVERSITY OF IOWA

    Estados Unidos, 1988

    Research assistant


 

Article (38)

The asymptotic behavior of the time fractional Schrödinger equation on Hilbert space
The time fractional Schrödinger equation with a non linearity of Hartree-type
A Laplace transform approach to linear equations with infinitely many derivatives and zeta-nonlocal field equations.
Nonlinear pseudo-differential equations defined by elliptic symbols on Lp and the fracctional Laplacian
The time fractional Schrödinger equation on Hilbert space
Differential Equations with Infinitely Many Derivatives and the Borel Transform
Nonlinear Evolution Equations with Infinitely Many Derivatives
NEW RESULTS FROM OLD INVESTIGATION: A NOTE ON FRACTIONAL m-DIMENSIONAL DIFFERENTIAL OPERATORS. THE FRACTIONAL LAPLACIAN
Parabolic flow on metric measure spaces
Separation dichotomy and wavefronts for a nonlinear convolution equation.
On a General Class of Nonlocal Equations
Some results on Laplace-Stieltjes transform
The initial value problem for ordinary differential equations with infinitely many derivatives
Nonlinear Equations with Infinitely many Derivatives
Completeness in quantum mechanics and the Weyl-Titchmarsh-Kodaira theorem
Fractional relaxation equations on Banach spaces
Functional calculus via Laplace transform and equations with infinitely many derivatives
On duality and spectral properties of (a, k)-regularized resolvents
Stability properties for solution operators
On the asymptotic behavior of regularized operator farnilies
Singular perturbation for Volterra equations of convolution type
Singular perturbations of integro-differential equations
Resonances for Hamiltonians with a delta perturbation in one dimension
Rates of approximation and ergodic limits of regularized operator families
Gaussian bounds for reduced heat kernels of subelliptic operators on nilpotent lie groups
Mean Quantum Sojourn Time
The vector-valued Stieltjes transform
The vector-valued Stieltjes transform
Asymptotic behavior of reduced dynamics on Hilbert sapces
Large time behavior for discontinuous dynamics on Hilbert spaces
Large time behavior of discontinuous dynamics on Hilbert spaces.
Reduced Weil models and representations of Gl(2,R)
Reduced Weil models for representations of GL(2, ?) and Barnes' lemma
Sur les temps moyens de séjour quantiques.
Reflection positivity for unitary representations of Lie groups.
A geometric construction of local representations of local Lie groups.
Spectral properties for operators in a Lie algebra.
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]

BookSection (6)

The Laplace Transform and nonlocal Field Equations
Generalized euclidean bosonic string equations
Generalized Euclidean bosonic string equations. Spectral analysis of quantum Hamiltonians
Existence of nonnegative solutions for generalized p-Laplacians
Norm estimates for a class of semigroups of Schrödinger type
Integral transform and ordirary differential equations of infinite order

ConferencePaper (4)

The Laplace Transform and Nonlocal Field Equations
On equations with infinitely many derivatives: integral transforms and the Cauchy problem
The Laplace Transform in the Study of Equations with Infinitely Many Derivatives
Exponential decay for perturbations of pure point hamiltonians

Proyecto (13)

On NonLinear Pseudo Differential Equations=> Equations with Infinitely Many Derivatives and Non Local Equations
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
68
Humberto Prado

Full Professor

Mathemnatics and Computer Sciences

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

13
Carlos Lizama

Full Professor

Matematica y Ciencia de la Computación

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

12
Enrique Reyes

Associate Professor

Mathematics and Computer Science

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

2
Guillermo Palma

Academico Jornada Completa

Departamento de Fisica

UNIVERSIDAD DE SANTIAGO DE CHILE

Santiago, Chile

1
Rolando Rebolledo

Full Professor

Universidad de Valparaíso/Facultad de Ingeniería

Valparaíso, Chile