Results 41 to 50 of about 82 (56)

Note on the Spectral Theorem [PDF]

arXiv, 2012
In this note, we show that the spectral theorem, has two representations; the Stone-von Neumann representation and one based on the polar decomposition of linear operators, which we call the deformed representation. The deformed representation has the advantage that it provides an easy extension to all closed densely defined linear operators on Hilbert
arxiv  

Existence and Asymptotics of Abstract Functional Differential Equations [PDF]

arXiv, 2017
It is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear abstract functional differential equations in both, the finite and infinite delay case. A generalization of the integral solution will provide regularity results. Moreover, this method applies to derive uniform convergence on the halfline,
arxiv  

Whole Line Solutions to Abstract Functional Differential Equations [PDF]

arXiv, 2017
In the underlying study it is shown how the linear method of the Yosida-approximation of the derivative applies to solve possibly nonlinear and multivalued functional differential equations like: \begin{eqnarray*} u^\prime(t) &\in& A(t,u_t)u(t) +\omega u(t), \ t \in \mathbb{R} \end{eqnarray*} Furthermore, in the case of finite and infinite delay we ...
arxiv  

A New Approach to Variational Inequalities of Parabolic Type [PDF]

arXiv, 2017
This paper is concerned with the weak solvability of fully nonlinear parabolic variational inequalities with time dependent convex constraints. As possible approaches to such problems, there are for instance the time-discretization method and the fixed point method of Schauder type with appropriate compactness theorems.
arxiv  

Regularizing effect of homogeneous evolution equations: case homogeneous order zero [PDF]

arXiv, 2019
In this paper, we develop a functional analytical theory for establishing that mild solutions of first-order Cauchy problems involving homogeneous operators of order zero are strong solutions; in particular, the first-order time derivative satisfies a global regularity estimate depending only on the initial value and the positive time.
arxiv  

Regularity and Separation for $p$-Laplace operators [PDF]

arXiv
We analyze $p$-Laplace operators with degenerate elliptic coefficients. This investigation includes Gru\v{s}in type $p$-Laplace operators. We describe a \emph{separation phenomenon} in elliptic and parabolic $p$-Laplace type equations, which provides an illuminating illustration of simple jump discontinuities of the corresponding weak solutions ...
arxiv  

Adjoint Operators on Banach Spaces [PDF]

arXiv, 2010
In this paper, we report on new results related to the existence of an adjoint for operators on separable Banach spaces and discuss a few interesting applications. (Some results are new even for Hilbert spaces.) Our first two applications provide an extension of the Poincar\'{e} inequality and the Stone-von Neumann version of the spectral theorem for a
arxiv  

The Schrödinger semigroup on some flat and non flat manifolds [PDF]

arXiv, 2011
In this paper we apply known techniques from semigroup theory to the Schr\"odinger problem with initial conditions. To this end, we define the regularized Schr\"odinger semigroup acting on a space-time domain and show that it is strongly continuous and contractive in $L_p,$ with $3/2 < p < 3.$ These results can easily be extended to the case of ...
arxiv  

A system of nonlinear set valued variational inclusions. [PDF]

Springerplus, 2014
Tang YK, Chang SS, Salahuddin S.
europepmc   +1 more source

Strong convergence theorems for a common zero of a finite family of H-accretive operators in Banach space. [PDF]

Springerplus, 2016
He H, Liu S, Chen R.
europepmc   +1 more source