arXiv subjects

Alon Ivtsan

Publications and source records attributed to Alon Ivtsan.

4 recordsLinked to original sources

arXiv2016

Variance of Resistance of "Line-Circle-Line" Graphs

We find the order of the variance of the growth model $X_{n+1} = X_n+X'_n + f(X''_n,X'''_n)$, where all the variables $X_n,X'_n,X''_n$ and $X'''_n$ are i.i.d., $X_0$ takes the values $1$ and $2$ with equal probability and $f$ is positive, monotone non-decreasing and satisfies conditions which, roughly speaking, pertain to its first and second order partial derivatives. For an appropriate choice of $f$ we obtain that the variance of the effective resistance between the endpoints of the "line-circle-line" graph $G_n$ is of order $\bigl(2 + \frac{1}{8} + {\scriptscriptstyle\mathcal{O}} (1)\bigr)^n$.

math.PR↗

arXiv2010

Stafney's lemma holds for several "classical" interpolation methods

Let (B_0,B_1) be a Banach pair. Stafney showed that one can replace the space F(B_0,B_1) with its subspace G(B_0,B_1) in the definition of the norm in the Calderon complex interpolation method on the strip if the element belongs to the intersection of the spaces B_i. We shall extend this result to a more general setting, which contains well-known interpolation methods: the Calderon complex interpolation method on the annulus, the Lions-Peetre real method (with several different choices of norms), and the Peetre "plus minus" method.

math.FA↗

arXiv2009

Interpolation of compact Lipschitz operators

Let (A_0,A_1) and (B_0,B_1) be Banach couples such that A_0 is contained in A_1 and (B_0,B_1) satisfies Arne Persson's approximation condition (H). Let T:A_1 --> B_1 be a possibly nonlinear Lipschitz mapping which also maps A_0 into B_0 and satisfies the following quantitative compactnesss condition: Ta \in ||a||_{A_0} K for each a \in A_0, where K is a fixed compact subset of B_0. We show that T maps the real interpolation space (A_0,A_1)_{θ,p} compactly into its counterpart (B_0,B_1)_{θ,p} for each θ\in (0,1) and p \in [1,\infty].

math.FA↗

arXiv2009

Counterexamples for interpolation of compact Lipschitz operators

Let (A_0,A_1) and (B_0,B_1) be Banach couples with A_0 contained in A_1 and B_0 contained in B_1. Let T:A_1 --> B_1 be a possibly nonlinear operator which is a compact Lipschitz map of A_j into B_j for j=0,1. It is known that T maps the Lions-Peetre space (A_0,A_1)_θ,q boundedly into (B_0,B_1)_θ,q for each θin (0,1) and each q in [1,\infty), and that this map is also compact if if T is linear. We present examples which show that in general the map T:(A_0,A_1)_θ,q --> (B_0,B_1)_θ,q is not compact.

math.FA↗