Antonelli, Gioacchino; Le Donne, Enrico(Springer, 2022)
We generalize both the notion of polynomial functions on Lie groups and the notion of horizontally affine maps on Carnot groups. We fix a subset S of the algebra g of left-invariant vector fields on a Lie group G and we ...
Tämän tutkielman sisältö voidaan karkeasti jakaa kahteen osaan. Ensimmäisessä on tarkoituksena tarkastella polynomimatriiseja ja erityisesti osoittaa toimiviksi kaksi niiden muokkaamiseen soveltuvaa algoritmia. Algoritmit ...
Kuca, Borys; Orponen, Tuomas; Sahlsten, Tuomas(Oxford University Press (OUP), 2023)
We prove that there exists a constant ϵ>0ϵ>0 with the following property: if K⊂R2K⊂R2 is a compact set that contains no pair of the form {x,x+(z,z2)}{x,x+(z,z2)} for z≠0z≠0, then dimHK≤2−ϵdimHK≤2−ϵ.
For a polynomial progression (x, x + P1(y), . . . , x + Pt(y)), we define four notions of complexity: Host Kra complexity, Weyl complexity, true complexity and algebraic complexity. The first two describe the smallest ...
