A. Iosevich

activity

19992005

most citedFalconer conjecture in the plane for random metrics

2 citations · 3 across the 6 of their papers we have counts for

collaborators

Showing 2001Show all

6 papers · 1 filter

math.CA2001

Fourier transform, $L^{2}$ restriction theorem, and scaling

Alex Iosevich

We show, using a Knapp-type homogeneity argument, that the $(L^{p}, L^{2})$ restriction theorem implies a growth condition on the hypersurface in question. We further use this result t…

math.CA2001

Maximal averages over flat radial hypersurfaces

Alex Iosevich

We prove nearly sharp Orlicz space estimates for maximal averages over flat radial hypersurfaces in $R^{d}$ , $d \geq 3$ .

math.CA2001

Some sharp restriction theorems for homogeneous manifolds

Laura DeCarli, Alex Iosevich

We prove some restriction theorems for flat homogeneous surfaces of codimension greater than one.

math.CA2001

How large are the spectral gaps?

Alex Iosevich, Steen Pedersen

Let $D$ be a bounded domain in $R^{n}$ whose boundary has a Minkowski dimension $α < n$ . Suppose that $E_{Λ} = {e^{2 π i x \cdot λ}}_{λ \in Λ}$ , $Λ$ an infinite discrete subset o…

math.CA2001

Fourier bases and a distance problem of Erd\H os

Alex Iosevich, Nets Katz, Steen Pedersen

We prove that no ball admits a non-harmonic orthogonal basis of exponentials. We use a combinatorial result, originally studied by Erd\H os, which says that the number of distances…

math.CA2001

Fuglede conjecture holds for convex planar domains

Alex Iosevich, Nets Katz, Terry Tao

Let $Ω$ be a compact convex domain in the plane. We prove that $L^{2} (Ω)$ has an orthogonal basis of exponentials if and only if $Ω$ tiles the plane by translation.

Fourier transform, L2 restriction theorem, and scaling

Maximal averages over flat radial hypersurfaces

Some sharp restriction theorems for homogeneous manifolds

How large are the spectral gaps?

Fourier bases and a distance problem of Erd\H os

Fuglede conjecture holds for convex planar domains

Fourier transform, $L^{2}$ restriction theorem, and scaling