In this paper, we introduce a wide class of space-fractional and time-fractional semidiscrete Dirac operators Lévy–Leblond type on the space-time lattice h Z n × [ 0 , ∞ ) $h{\mathbb {Z}}^n\times [0,\infty )$ ( > $h>0$ ), resembling to fractional counterparts so-called parabolic operators. The methods adopted here are fairly operational, relying mostly algebraic manipulations involving Clifford...

t∈α xt : α ∈ Pf (ω)}. A set A ⊆ N is called an IP-set iff there exists a sequence 〈xn〉n=0 in N such that FS(〈xn〉n=0) ⊆ A. (This definitions make perfect sense in any semigroup (S, ·) and we indeed plan to use them in this context. FS is an abbriviation of finite sums and will be replaced by FP if we use multiplicative notation for the semigroup operation.) Now Hindman’s Theorem states that in a...

t∈α xt : α ∈ Pf (ω)}. A set A ⊆ N is called an IP-set iff there exists a sequence 〈xn〉n=0 in N such that FS(〈xn〉n=0) ⊆ A. (This definitions make perfect sense in any semigroup (S, ·) and we indeed plan to use them in this context. FS is an abbriviation of finite sums and will be replaced by FP if we use multiplicative notation for the semigroup operation.) Now Hindman’s Theorem states that in a...

The semigroup DV of digraphs on a set V of n labeled vertices is defined. It is shown that DV is faithfully represented by the semigroup Bn of n × n Boolean matrices and that the Green’s L, R, H, and D equivalence classifications of digraphs in DV follow directly from the Green’s classifications already established for Bn. The new results found from this are: (i) L, R, and H equivalent digraphs...

A free semigroup algebra is the wot-closed algebra generated by an n-tuple of isometries with pairwise orthogonal ranges. The interest in these algebras arises primarily from two of their interesting features. The first is that they provide useful information about unitary invariants of representations of the Cuntz–Toeplitz algebras. The second is that they form a class of nonself-adjoint opera...

If T is a numerical semigroup with maximal ideal N , define associated semigroups B(T ) := (N −N) and L(T ) = ∪{(hN −hN) : h ≥ 1}. If S is a numerical semigroup, define strictly increasing finite sequences {Bi(S) : 0 ≤ i ≤ β(S)} and {Li(S) : 0 ≤ i ≤ λ(S)} of semigroups by B0(S) := S =: L0(S), Bβ(S)(S) := N =: Lλ(S)(S), Bi+1(S) := B(Bi(S)) for 0 < i < β(S), Li+1(S) := L(Li(S)) for 0 < i < λ(S). ...

Bibliography 75 Index 77 v Introduction Evolution means the change of a certain system with respect to time. In a more suggestive language, one could talk of the " motion " of a system in time. Examples could be the movement of planets, the growth of a population, ... From a philosophical point of view (cf. G. Nickel in [9]) it turns out, that the right mathematical model for evolution is a one...

We study elliptic and parabolic problems governed by the singular operatorsL=yα1Δx+yα2(Dyy+cyDy−by2),α1,α2∈R in half-space R+N+1={(x,y):x∈RN,y>0}. prove Lp-estimates solvability for associated problems. In language of semigroup theory, we that L generates an analytic semigroup, characterize its domain as a weighted Sobolev space show it has maximal regularity.

We study dispersive mixed-order systems of pseudodifferential operators in the setting of Lp-Sobolev spaces. Under the weak condition of quasihyperbolicity, these operators generate a semigroup in the space of tempered distributions. However, if the basic space is a tuple of Lp-Sobolev spaces, a strongly continuous semigroup is in many cases only generated if p = 2 or n = 1. The results are app...

This is an abridged diary of some of thèmathematical adventures' we encountered on our way towards a proof of the Divisibility Conjecture, formulated below. In this section we give a brief account of how Porcupine Varieties enter the stage naturally in connection with the Divisibility Problem. Let us start with some basic concepts and the appropriate notation from 5]. Let G be a connected Lie g...