This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of input data. We present several theoretical results that explain the relation between the different definitions. Additionally, results on the orthogonality of the decomposition, a Parsevaltype identity...

In this paper we parallelly build up the theories of normed linear spaces and of linear spaces with indefinite metric, called also Minkowski spaces for finite dimensions in the literature. In the first part of this paper we collect the common properties of the semi-and indefinite-inner-products and define the semi-indefinite-inner-product and the corresponding structure, the semi-indefinite-inn...

An elliptic equation of order 2m with general nonlocal boundary-value conditions, in a plane bounded domain G with piecewise smooth boundary, is considered. Generalized solutions belonging to the Sobolev space Wm 2 (G) are studied. The Fredholm property of the unbounded operator corresponding to the elliptic equation, acting on L2(G), and defined for functions from the space Wm 2 (G) that satis...

in this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in cat(0) spaces as well as in uced banach spaces. moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...

Some generalized soliton solutions of the cosmological Einstein-Rosen type defined in the space-time region t 2;prin terms of canonical coordinates are considered. Vacuum solutions are studied and interpreted as cosmological models. Fluid solutions are also considered and are seen to represent inhomogeneous cosmological models that become homogeneous at t 00. A subset of these evolve toward iso...

The 2-parameter family of certain homogeneous Lorentzian 3-manifolds, which includes Minkowski 3-space and anti-de Sitter 3-space, is considered. Each 3-manifold in the has a solvable Lie group structure with left invariant metric. A generalized integral representation formula for maximal spacelike surfaces 3-manifolds obtained. normal Gauß map its harmonicity are discussed.

In this paper, we look at the notion of cohomological triviality fibrations homogeneous spaces affine algebraic groups defined over \({\mathbb {C}}\) and use topological methods, primarily theory covering spaces. This is made possible because structure groups. Further, generalize our results for arbitrary connected their As an application give a result quasi- reductive (i.e., whose unipotent ra...