Search results for " mathematical physics"
showing 10 items of 396 documents
Bounded compositions on scaling invariant Besov spaces
2012
For $0 < s < 1 < q < \infty$, we characterize the homeomorphisms $��: \real^n \to \real^n$ for which the composition operator $f \mapsto f \circ ��$ is bounded on the homogeneous, scaling invariant Besov space $\dot{B}^s_{n/s,q}(\real^n)$, where the emphasis is on the case $q\not=n/s$, left open in the previous literature. We also establish an analogous result for Besov-type function spaces on a wide class of metric measure spaces as well, and make some new remarks considering the scaling invariant Triebel-Lizorkin spaces $\dot{F}^s_{n/s,q}(\real^n)$ with $0 < s < 1$ and $0 < q \leq \infty$.
SPECTRAL INVARIANCE FOR CERTAIN ALGEBRAS OF PSEUDODIFFERENTIAL OPERATORS
2001
We construct algebras of pseudodifferential operators on a continuous family groupoid G that are closed under holomorphic functional calculus, contain the algebra of all pseudodifferential operators of order 0 on G as a dense subalgebra, and reflect the smooth structure of the groupoid G, when G is smooth. As an application, we get a better understanding on the structure of inverses of elliptic pseudodifferential operators on classes of non-compact manifolds. For the construction of these algebras closed under holomorphic functional calculus, we develop three methods: one using two-sided semi-ideals, one using commutators, and one based on Schwartz spaces on the groupoid.
Character correspondences in blocks with normal defect groups
2014
Abstract In this paper we give an extension of the Glauberman correspondence to certain characters of blocks with normal defect groups.
Artin monoids inject in their groups
2001
We prove that the natural homomorphism from an Artin monoid to its associated Artin group is always injective
On base loci of higher fundamental forms of toric varieties
2019
We study the base locus of the higher fundamental forms of a projective toric variety $X$ at a general point. More precisely we consider the closure $X$ of the image of a map $({\mathbb C}^*)^k\to {\mathbb P}^n$, sending $t$ to the vector of Laurent monomials with exponents $p_0,\dots,p_n\in {\mathbb Z}^k$. We prove that the $m$-th fundamental form of such an $X$ at a general point has non empty base locus if and only if the points $p_i$ lie on a suitable degree-$m$ affine hypersurface. We then restrict to the case in which the points $p_i$ are all the lattice points of a lattice polytope and we give some applications of the above result. In particular we provide a classification for the se…
Multiplicity of ground states for the scalar curvature equation
2019
We study existence and multiplicity of radial ground states for the scalar curvature equation $$\begin{aligned} \Delta u+ K(|x|)\, u^{\frac{n+2}{n-2}}=0, \quad x\in {{\mathbb {R}}}^n, \quad n>2, \end{aligned}$$when the function $$K:{{\mathbb {R}}}^+\rightarrow {{\mathbb {R}}}^+$$ is bounded above and below by two positive constants, i.e. $$0 0$$, it is decreasing in (0, 1) and increasing in $$(1,+\infty )$$. Chen and Lin (Commun Partial Differ Equ 24:785–799, 1999) had shown the existence of a large number of bubble tower solutions if K is a sufficiently small perturbation of a positive constant. Our main purpose is to improve such a result by considering a non-perturbative situation: we ar…
The Heat Content for Nonlocal Diffusion with Non-singular Kernels
2017
Abstract We study the behavior of the heat content for a nonlocal evolution problem.We obtain an asymptotic expansion for the heat content of a set D, defined as ℍ D J ( t ) := ∫ D u ( x , t ) 𝑑 x ${\mathbb{H}_{D}^{J}(t):=\int_{D}u(x,t)\,dx}$ , with u being the solution to u t = J ∗ u - u ${u_{t}=J\ast u-u}$ withinitial condition u 0 = χ D ${u_{0}=\chi_{D}}$ . This expansion is given in terms of geometric values of D. As a consequence, we obtain that ℍ D J ( t ) = | D | - P J ( D ) t + o ( t ) ${\mathbb{H}^{J}_{D}(t)=\lvert D\rvert-P_{J}(D)t+o(t)}$ as t ↓ 0 ${t\downarrow 0}$ .We also recover the usual heat content for the heat equation when we rescale the kernel J in an appro…
Instability of Equilibrium States for Coupled Heat Reservoirs at Different Temperatures
2007
Abstract We consider quantum systems consisting of a “small” system coupled to two reservoirs (called open systems). We show that such systems have no equilibrium states normal with respect to any state of the decoupled system in which the reservoirs are at different temperatures, provided that either the temperatures or the temperature difference divided by the product of the temperatures are not too small. Our proof involves an elaborate spectral analysis of a general class of generators of the dynamics of open quantum systems, including quantum Liouville operators (“positive temperature Hamiltonians”) which generate the dynamics of the systems under consideration.
Three dimensional reductions of four-dimensional quasilinear systems
2017
In this paper we show that integrable four dimensional linearly degenerate equations of second order possess infinitely many three dimensional hydrodynamic reductions. Furthermore, they are equipped infinitely many conservation laws and higher commuting flows. We show that the dispersionless limits of nonlocal KdV and nonlocal NLS equations (the so-called Breaking Soliton equations introduced by O.I. Bogoyavlenski) are one and two component reductions (respectively) of one of these four dimensional linearly degenerate equations.
Affine Surfaces With a Huge Group of Automorphisms
2013
We describe a family of rational affine surfaces S with huge groups of automorphisms in the following sense: the normal subgroup Aut(S)alg of Aut(S) generated by all algebraic subgroups of Aut(S) is not generated by any countable family of such subgroups, and the quotient Aut(S)/Aut(S)alg cointains a free group over an uncountable set of generators.