Abstract Let G be a locally compact unimodular group, and let $\phi $ some function of n variables on . To such , one can associate multilinear Fourier multiplier, which acts -fold product the noncommutative $L_p$ -spaces group von Neumann algebra. One may also define an associated Schur Schatten classes $S_p(L_2(G))$ We generalize well-known transference results from linear case to case. In pa...

The terminology and notation used here have been introduced in the following articles: [12], [13], [2], [3], [9], [1], [6], [11], [14], [4], [18], [7], [8], [5], [19], [10], [16], [17], and [15]. For simplicity, we use the following convention: a, x are real numbers, n is an element of N, A is a closed-interval subset of R, f , h, f1, f2 are partial functions from R to R, and Z is an open subse...

subject to the initial condition xðt0Þ 1⁄4 x0; t0 $ 0; x0 [ R; ð2Þ where f : 1⁄20;1Þ £ R ! R is a continuous function and t is from a so-called “time scale” T (which is a nonempty closed subset of R). Equation (1) subject to Eq. (2) is known as an initial value problem (IVP) on time scales. If T 1⁄4 R then x 1⁄4 x 0 and Eqs. (1) and (2) become the following IVP for ordinary differential equatio...

We study some properties of positive solutions to the higher order conformally invariant equation with a singular set $$\begin{aligned} (-\Delta )^m u = u^{\frac{n+2m}{n-2m}} ~~~~~~ \text {in} ~ \Omega \backslash \Lambda , \end{aligned}$$ where $$\Omega \subset {\mathbb {R}}^n$$ is an open domain, $$\Lambda $$ closed subset $${\mathbb $$1 \le m < n/2$$ and integer. first establish local estimat...

We consider the problem of computing the minimum of a polynomial function g on a basic closed semialgebraic set E ⊂ R. We present a probabilistic symbolic algorithm to find a finite set of sample points of the subset E of E where the minimum of g is attained, provided that E is non-empty and has at least one compact connected component.

We investigate finite torsors over big opens of spectra strongly $F$-regular germs that do not extend to the whole spectrum. Let $(R,\mathfrak{m},k)$ be a $k$-germ where $k$ is an algebraically closed field characteristic $p>0$. prove existence local cover $R \subset R^{\star}$ so $R^{\star}$ and: for all algebraic groups $G/k$ with solvable neutral component, every $G$-torsor open $\mathrm{Spe...

Given any finite subset X of the sphere S, n ≥ 2, which includes no pairs of antipodal points, we explicitly construct smoothly immersed closed orientable hypersurfaces in Euclidean space R whose Gauss map misses X. In particular, this answers a question of M. Gromov.

We provide a specific representation of convex polynomials nonnegative on a convex (not necessarily compact) basic closed semi-algebraic set K ⊂ R. Namely, they belong to a specific subset of the quadratic module generated by the concave polynomials that define K. Mathematics Subject Classification (2000). Primary 14P10; Secondary 11E25 12D15 90C25.