Search results for "Mathematical analysis"

On essential maximality of linear pseudo-differential operators

1989

Sur une classe d’equations du type parabolique lineaires

1996

The application of the variational method for the existence theorem, developped by J. L. Lions, for the evolution equations in Hilbert spaces to a considerably large class of systems of linear partial differential equations of parabolic type is studied by defining Hilbert spaces in relation to the elliptic operator of the system, and an example insired by the system of equations for a viscous gas is examined.

On Determinants of Integrable Operators with Shifts

2013

Integrable integral operator can be studied by means of a matrix Riemann--Hilbert problem. However, in the case of so-called integrable operators with shifts, the associated Riemann--Hilbert problem becomes operator valued and this complicates strongly the analysis. In this note, we show how to circumvent, in a very simple way, the use of such a setting while still being able to characterize the large-$x$ asymptotic behavior of the determinant associated with the operator.

Explicit form of the time operator of a gaussian stationary process

2004

We present the time operator theory in the framework of stationary stochastic processes. The main results of the paper is the derivation of the time operator acting on the Fock space associated with a discrete time gaussian stationary process.

Elliptic 1-Laplacian equations with dynamical boundary conditions

2018

Abstract This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle. Our main theorem shows that the solution we found is actually a strong solution. We also compare solutions with different data.

On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields

1986

Consider a fami ly of vector fCelds x~ on the plane. This fami ly depends on a parameter ~ ~ /R A, for some A ~ /~, and is supposed to be 0 ~ in (m,~) 6 /i~ 2X /~A. Suppose that for ~ = O, the vector f i e l d X o has a separatrix loop. This means that X o has an hyperbol ic saddle point s o and that one of the stable separatr ix of 8 o coincides with one of the unstable one. The union of th is curve and s o is the loop ?. A return map is defined on one side of r .

Interpolating sequences for bounded analytic functions

2007

. We prove that any sequence in the open ball of a complex Banach space E, even in that of E**, whose norms are an interpolating sequence for H∞, is interpolating for the space of all bounded analytic functions on BE-The construction made yields that the interpolating functions depend linearly on the interpolated values.

A bilinear version of Orlicz–Pettis theorem

2008

Abstract Given three Banach spaces X, Y and Z and a bounded bilinear map B : X × Y → Z , a sequence x = ( x n ) n ⊆ X is called B -absolutely summable if ∑ n = 1 ∞ ‖ B ( x n , y ) ‖ Z is finite for any y ∈ Y . Connections of this space with l weak 1 ( X ) are presented. A sequence x = ( x n ) n ⊆ X is called B -unconditionally summable if ∑ n = 1 ∞ | 〈 B ( x n , y ) , z ∗ 〉 | is finite for any y ∈ Y and z ∗ ∈ Z ∗ and for any M ⊆ N there exists x M ∈ X for which ∑ n ∈ M 〈 B ( x n , y ) , z ∗ 〉 = 〈 B ( x M , y ) , z ∗ 〉 for all y ∈ Y and z ∗ ∈ Z ∗ . A bilinear version of Orlicz–Pettis theorem is given in this setting and some applications are presented.

A class of quasi-Newton generalized Steffensen methods on Banach spaces

2002

AbstractWe consider a class of generalized Steffensen iterations procedure for solving nonlinear equations on Banach spaces without any derivative. We establish the convergence under the Kantarovich–Ostrowski's conditions. The majorizing sequence will be a Newton's type sequence, thus the convergence can have better properties. Finally, a numerical comparation with the classical methods is presented.

A Variational Formulation of the BEM for Elastic-Plastic Analysis

1990

The quasi-static elastic perfectly plastic analysis problem is approached by the boundary element method (BEM). To this purpose, a time semidiscretization is first achieved by finite intervals (Fl) in order to transform, through a variationally consistent procedure, the evolutive problem into a discrete sequence of inelastic holonomic-type “weighted” problems for each of which a mixed boundary/domain min-max principle is established. This principle is then discretized by means of boundary elements (BE) and cell elements (CE), the latter having the only purpose of suitably interpolating the FI weighted yielding laws within the domain. The algebraic governing equations obtained show symmetry …