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Person# Joachim Stubbe

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Schrödinger equation

The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. Its discovery was a significant landmark in the development of quantu

Eigenvalues and eigenvectors

In linear algebra, an eigenvector (ˈaɪgənˌvɛktər) or characteristic vector of a linear transformation is a nonzero vector that changes at most by a constant factor when that linear transformation is

Variational principle

In science and especially in mathematical studies, a variational principle is one that enables a problem to be solved using calculus of variations, which concerns finding functions that optimize the

Courses taught by this person (3)

MATH-201: Analysis III

Calcul différentiel et intégral: Eléments d'analyse vectorielle, intégration par partie, intégrale curviligne, intégrale de surface, théorèmes de Stokes, Green, Gauss, fonctions harmoniques;
Eléments d'analyse complexe: fonctions holomorphes ou analytiques, théorème des résidus et applications

MATH-206: Analysis IV

Donner une introduction aux concepts, méthodes et techniques de l'intégrale de Lebesgue, de l'analyse dans des espaces vectoriels de dimension infinie et de la théorie des opérateurs.

MATH-303: Measure and integration

On introduit la théorie abstraite des espaces de mesure et on traite rigoureusement la mesure de Lebesgue et ensuite l'intégrale de Lebesgue.

People doing similar research (44)

Paolo Luzzini, Luigi Provenzano, Joachim Stubbe

In this paper, we consider the first eigenvalue.1(O) of the Grushin operator.G :=.x1 + |x1|2s.x2 with Dirichlet boundary conditions on a bounded domain O of Rd = R d1+ d2. We prove that.1(O) admits a unique minimizer in the class of domains with prescribed finite volume, which are the cartesian product of a set in Rd1 and a set in Rd2, and that the minimizer is the product of two balls Omega(*)(1).subset of R-d1 and O-* (2)subset of R-d2. Moreover, we provide a lower bound for | Omega(*) (1) | and for lambda(1)( O-* (1) x O-* (2)). Finally, we consider the limiting problem as s tends to 0 and to +8.

Luigi Provenzano, Joachim Stubbe

We present asymptotically sharp inequalities, containing a 2nd term, for the Dirichlet and Neumann eigenvalues of the Laplacian on a domain, which are complementary to the familiar Berezin-Li-Yau and Kroger inequalities in the limit as the eigenvalues tend to infinity. We accomplish this in the framework of the Riesz mean R-1(z) of the eigenvalues by applying the averaged variational principle with families of test functions that have been corrected for boundary behaviour.

Related units (4)