scholarly journals Multilevel decompositions and norms for negative order Sobolev spaces

2021 ◽  
pp. 1
Author(s):  
Thomas Führer
2019 ◽  
Vol 39 (1) ◽  
pp. 553-583 ◽  
Author(s):  
Rowan Killip ◽  
◽  
Satoshi Masaki ◽  
Jason Murphy ◽  
Monica Visan ◽  
...  

2019 ◽  
Vol 30 (08) ◽  
pp. 1950034 ◽  
Author(s):  
Hyunsu Ha ◽  
Gihyun Lee ◽  
Raphaël Ponge

This paper is the second part of a two-paper series whose aim is to give a detailed description of Connes’ pseudodifferential calculus on noncommutative [Formula: see text]-tori, [Formula: see text]. We make use of the tools introduced in the 1st part to deal with the main properties of pseudodifferential operators on noncommutative tori of any dimension [Formula: see text]. This includes the main results mentioned in [2, 5, 11]. We also obtain further results regarding action on Sobolev spaces, spectral theory of elliptic operators, and Schatten-class properties of pseudodifferential operators of negative order, including a trace-formula for pseudodifferential operators of order [Formula: see text].


2013 ◽  
Vol 15 (06) ◽  
pp. 1350005
Author(s):  
XAVIER CARVAJAL PAREDES ◽  
RICARDO A. PASTRAN

We establish local well-posedness in Sobolev spaces Hs(𝕋), with s ≥ -1/2, for the initial value problem issues of the equation [Formula: see text] where η > 0, (Lu)∧(k) = -Φ(k)û(k), k ∈ ℤ and Φ ∈ ℝ is bounded above. Particular cases of this problem are the Korteweg–de Vries–Burgers equation for Φ(k) = -k2, the derivative Korteweg–de Vries–Kuramoto–Sivashinsky equation for Φ(k) = k2 - k4, and the Ostrovsky–Stepanyams–Tsimring equation for Φ(k) = |k| - |k|3.


Author(s):  
V. V. Makarov ◽  
D. A. Lozovoy

  Enzootic bovine leucosis (EBL) has been known for more than a century and a half. Its occurrence and registration may have historically been associated with intensive breeding of dairy cattle in Western Europe to increase target productivity. It is known that any limiting intervention in the nature of the animal organism is always accompanied by an uncontrolled and unpredictable change in the genotype of a wider range than the required, particularly negative order. In particular, a decrease in the resistance to macroorganisms and the possibility of the new diseases emergence, including infectious ones (for example, immunodeficiencies such as BLAD syndrome of black-motley cattle and stress syndrome in pigs, the occurrence of scrapie and other slow sheep infections). In the last two decades of the last century, in many disadvantaged countries, primarily Western European, national programs for the eradication of EBL have been developed and subsequently successfully implemented. First of all the motivation was the economy of dairy cattle breeding (mainly the extension of productive age, as well as the tightening of requirements in international trade in cattle and bull products, breeding, pricing, etc.). In an analytical article are reviewed the elements of epizootology of EBL in the foreign countries with special attention to the situation in the USA, scenarios of various control programs, and promising methods for assessing the role of infected animals in the epizootic process. A critical assessment of the problem of EBL in the Russian Federation is given, the reasons for the ineffectiveness of against leucosis measures are discussed.


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