131,334 research outputs found
Cyclic Hilbert Spaces
No full textWe analyse in this paper a concept related to the Connes Embedding Problem [Co]. A type II1 algebra is an algebra with a trace, and CEP requires for the multiplication to be approximated by matrices. Here we start the analysis of four products, which is the study of cyclic Hilbert spaces
Free Group Factors and Hecke Operators
No full textThis is a note on Radulescu’s work taken by N. Ozawa. We first review the
construction of the classical Hecke operator and recall the Ramanujan–Petersson conjecture
about its spectrum. We then relate it to the study of a type II1 factor via Berezin
calculus
Progress in Nonlinear Kirchhoff Problems
No full textThis special issue contains some contributions written by leading experts in problems involving Kirchhoffoperators of various kinds. We feel particularly honored to have had the opportunity to write this special issue for the journal Nonlinear Analysisby Elsevier
Multiplicity of concentrating solutions for (p, q)-Schrödinger equations with lack of compactness
No full textWe study the multiplicity of concentrating solutions for the following class of (p, q)-Laplacian problems (Formula presented.) where ε > 0 is a small parameter, γ∈{0,1},1 infΛV for some bounded open set Λ ⊂ RN, and f: R → R is a continuous nonlinearity with subcritical growth. The main results are obtained by combining minimax theorems, penalization technique and Ljusternik–Schnirelmann category theory. We also provide a multiplicity result for a supercritical version of the above problem by combining a truncation argument with a Moser-type iteration. As far as we know, all these results are new
Fractional double-phase patterns: concentration and multiplicity of solutions
No full textWe consider the following class of fractional problems with unbalanced growth: {(−Δ)psu+(−Δ)qsu+V(εx)(|u|p−2u+|u|q−2u)=f(u)in RN,u∈Ws,p(RN)∩Ws,q(RN),u>0in RN, where ε>0 is a small parameter, s∈(0,1), [Formula presented], (−Δ)ts (with t∈{p,q}) is the fractional t-Laplacian operator, V:RN→R is a continuous potential satisfying local conditions, and f:R→R is a continuous nonlinearity with subcritical growth. Applying suitable variational and topological arguments, we obtain multiple positive solutions for ε>0 sufficiently small as well as related concentration properties, in relationship with the set where the potential V attains its minimum
Irreducible subfactors derived from Popa's construction for non-tracial state
No full textFor an inclusion of the form C⊆Mn(C)
, where M n (C) is endowed with a state with diagonal weights λ = (λ1, ..., λn), we use Popa’s construction, for non-tracial states, to obtain an irreducible inclusion of II1 factors, Nλ(Q)⊆Mλ(Q)
of index ∑1λi
. Mλ(Q) is identified with a subfactor inside the centralizer algebra of the canonical free product state on Q ⋆ M N (C). Its structure is described by “infinite” semicircular elements as in {xc[32]}.
The irreducible subfactor inclusions obtained by this method are similar to the first irreducible subfactor inclusions, of index in [{xc4},∞) constructed in {xc[24]}, starting with the Jones’ subfactors inclusion Rs⊆R
, s gt; 4. In the present paper, since the inclusion we start with has a simpler structure, it is easier to control the algebra structure of the subfactor inclusions.
If the weights correspond to a unitary, finite-dimensional representation of a Woronowicz’s compact quantum group G, then the factor Mλ(Q) is contained in the fixed point algebra of an action of the quantum group on Q ⋆ MN(C), with equality if G is SUq(N), (or SOq(3) when N = 2). By Takesaki duality, the factor Mλ(L(FN)) is Morita equivalent to
L
(F∞).
This method gives also another approach to find, as also recently proved in {xc[36]}, irreducible subfactors of
L
(F∞) for index values bigger than 4
The Corporate Tax Reform of 2008: Germany’s Answer to Globalization – or Just Patchwork?
No full textUnternehmensbesteuerung, Steuerreform, Wirtschaftliche Anpassung, Globalisierung, Wirtschaftspolitische Wirkungsanalyse, Deutschland, Corporate taxation, Tax reform, Economic adjustment, Globalization, Economic policy analysis, Germany
Variational problems on the Sphere
No full textBy various variational approaches we study the existence of infinitely many weak solutions for a nonlinear problem on the sphere
Blow-up solutions for fully nonlinear equations: Existence, asymptotic estimates and uniqueness
No full textThe primary objective of the paper is to study the existence, asymptotic boundary estimates and uniqueness of large solutions to fully nonlinear equations H (x, u, Du, D2u) = f(u) + h(x) in bounded C2 domains Ω ⊆ Rn. Here H is a fully nonlinear uniformly elliptic differential operator, f is a non-decreasing function that satisfies appropriate growth conditions at infinity, and h is a continuous function on Ω that could be unbounded either from above or from below. The results contained herein provide substantial generalizations and improvements of results known in the literature
Concentration of positive solutions for a class of fractional p-Kirchhoff type equations
No full textWe study the existence and concentration of positive solutions for the following class of fractional p-Kirchhoff type problems: 0 & where is a small positive parameter, a and b are positive constants, s (0, 1) and p (1, ∞) are such that, is the fractional p-Laplacian operator, f: → is a superlinear continuous function with subcritical growth and V: R3 → is a continuous potential having a local minimum. We also prove a multiplicity result and relate the number of positive solutions with the topology of the set where the potential V attains its minimum values. Finally, we obtain an existence result when f(u) = uq-1 + γur-1, where γ > 0 is sufficiently small, and the powers q and r satisfy 2p < q < ps≥ r. The main results are obtained by using some appropriate variational argument
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