Sökning: "the space of lattices"

Visar resultat 1 - 5 av 19 avhandlingar innehållade orden the space of lattices.

1. 1. Sobolev-Type Spaces : Properties of Newtonian Functions Based on Quasi-Banach Function Lattices in Metric Spaces

   Författare :Lukáš Malý; Anders Björn; Jana Björn; Tomas Sjödin; Andrea Cianchi; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Newtonian space; Sobolev-type space; metric measure space; upper gradient; Sobolev capacity; Banach function lattice; quasi-normed space; rearrangement-invariant space; maximal operator; Lipschitz function; regularization; weak boundedness; density of Lipschitz functions; quasi-continuity; continuity; doubling measure; Poincaré inequality;

   Sammanfattning : This thesis consists of four papers and focuses on function spaces related to first-order analysis in abstract metric measure spaces. The classical (i.e., Sobolev) theory in Euclidean spaces makes use of summability of distributional gradients, whose definition depends on the linear structure of Rn. LÄS MER

3. 2. Distributional Limit Theorems on the Space of Lattices

   Författare :Kristian Holm; Göteborgs universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES;

   Sammanfattning : .... LÄS MER

4. 3. A quantum for a quantum : Quantum simulators in exotic lattices

   Författare :Pil Maria Saugmann; Jonas Larson; André Eckardt; Stockholms universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; quantum physics; condensed matter physics; quantum optics; optical lattices. Fock state lattices; exotic lattices; frustration; Theoretical Physics; teoretisk fysik;

   Sammanfattning : This thesis centers on how to use exotic lattices in different ways to design potential quantum simulators. These exotic lattices are either real physical objects in the form of ultra cold atoms in  bipartite optical lattice systems or lattice models revealed in state space. LÄS MER

5. 4. Geometry of numbers, class group statistics and free path lengths

   Författare :Samuel Holmin; Pär Kurlberg; Yiannis Petridis; KTH; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; geometry of numbers; lattices; class numbers; class groups; free path lengths; Mathematics; Matematik;

   Sammanfattning : This thesis contains four papers, where the first two are in the area of geometry of numbers, the third is about class group statistics and the fourth is about free path lengths. A general theme throughout the thesis is lattice points and convex bodies. LÄS MER

7. 5. Newtonian Spaces Based on Quasi-Banach Function Lattices

   Författare :Lukáš Malý; Anders Björn; Jana Björn; Tomas Sjödin; Pekka Koskela; Linköpings universitet; []
   Nyckelord :NATURVETENSKAP; NATURAL SCIENCES; Newtonian space; upper gradient; weak upper gradient; Banach function lattice; quasi-normed space; metric measure space;

   Sammanfattning : The traditional first-order analysis in Euclidean spaces relies on the Sobolev spaces W1,p(Ω), where Ω ⊂ Rn is open and p ∈ [1, ∞].The Sobolev norm is then defined as the sum of Lp norms of a function and its distributional gradient.We generalize the notion of Sobolev spaces in two different ways. LÄS MER