in this paper, the maximal dissipative extensions of a symmetric singular 1d discrete hamiltonian operator with maximal deficiency indices (2,2) (in limit-circle cases at ±∞) and acting in the hilbert space ℓ_{ω}²(z;c²) (z:={0,±1,±2,...}) are considered. we consider two classes dissipative operators with separated boundary conditions both at -∞ and ∞. for each of these cases we establish a self...

The focus of this article is to develop computationally efficient mathematical morphology operators on hypergraphs. To this aim we consider lattice structures on hypergraphs on which we build morphological operators. We develop a pair of dual adjunctions between the vertex set and the hyper edge set of a hypergraph H , by defining a vertex-hyperedge correspondence. This allows us to recover the...

We provide an explicit normal distinguished boundary dilation to a pair of commuting operators (S, P ) having the closed symmetrized bidisc Γ as a spectral set. This is called Sz.-Nagy dilation of (S, P ). The operator pair that dilates (S, P ) is obtained by an application of Stinespring dilation of (S, P ) given by Agler and Young. We further prove that the dilation is minimal and the dilatio...

In classical mathematical morphology for scalar images, the natural ordering of grey levels is used to define the erosion/dilation and the derived operators. Various operators can be sequentially applied to the resulting images always using the same ordering. In this paper we propose to consider the result of a prior transformation to define the imaginary part of a complex image, where the real...

We construct monopole operators for 3d Yang-Mills-matter theories and Chern-Simons-matter in canonical formalism. In this framework, operators, although as the disorder could be written terms of fundamental fields theory, thus treated same way ordinary operators. study properties constructed theories, transform local with classical conformal dimension $ 0 under action dilation are also covarian...

We establish a finite-dimensional version of the Arveson-Stinespring dilation theorem for unital completely positive maps on operator systems. This result can be seen as general principle to deduce theorems from their classical infinite-dimensional counterparts. In addition providing unified proofs known theorems, we versions Agler's rational an annulus, Berger's operators numerical radius at m...

The semi-group of weighted composition operators (Wn)n≥1 whereWnf(z)=(1+z+…+zn−1)f(zn) on the classical Hardy-Hilbert space H2 open unit disk is related to Riemann Hypothesis (RH) (see [16]). semigroup also closely Invariant Subspace Problem (ISP) and Periodic Dilation Completeness (PDCP). We obtain results cyclic vectors, spectra, invariant reducing subspaces. In particular, we show that sever...