### An optimal estimate for extrapolation from a finite set in the Wiener class.

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Let $D\subset \subset {\u2102}^{n},n\ge 2$, be a domain with ${C}^{2}$-boundary and $K\subset \partial D$ be a compact set such that $\partial D\setminus K$ is connected. We study univalent analytic extension of CR-functions from $\partial D\setminus K$ to parts of $D$. Call $K$ CR-convex if its $A\left(D\right)$-convex hull, $A\left(D\right)-\mathrm{hull}\left(K\right)$, satisfies $K=\partial D\cap A\left(D\right)-\mathrm{hull}\left(K\right)$ ($A\left(D\right)$ denoting the space of functions, which are holomorphic on $D$ and continuous up to $\partial D$). The main theorem of the paper gives analytic extension to $\partial D\setminus A\left(D\right)-\mathrm{hull}\left(K\right)$, if $K$ is CR- convex.

Global time estimates of ${L}^{p}-{L}^{q}$ norms of solutions to general strictly hyperbolic partial differential equations are considered. The case of special interest in this paper are equations exhibiting the dissipative behaviour. Results are applied to discuss time decay estimates for Fokker-Planck equations and for wave type equations with negative mass.

In this paper we prove that the projective dimension of ${\mathcal{M}}_{n}={R}^{4}/\u27e8{A}_{n}\u27e9$ is $2n-1$, where $R$ is the ring of polynomials in $4n$ variables with complex coefficients, and $\u27e8{A}_{n}\u27e9$ is the module generated by the columns of a $4\times 4n$ matrix which arises as the Fourier transform of the matrix of differential operators associated with the regularity condition for a function of $n$ quaternionic variables. As a corollary we show that the sheaf $\mathcal{R}$ of regular functions has flabby dimension $2n-1$, and we prove a cohomology vanishing theorem for open...

In this paper we use Nachbin’s holomorphy types to generalize some recent results concerning hypercyclic convolution operators on Fréchet spaces of entire functions of bounded type of infinitely many complex variables

We prove, among other results, that $min(u,v)$ is plurisubharmonic (psh) when $u,v$ belong to a family of functions in $\mathrm{psh}\left(D\right)\cap {\Lambda}_{\alpha}\left(D\right),$ where ${\Lambda}_{\alpha}\left(D\right)$ is the $\alpha $-Lipchitz functional space with $1<\alpha <2.$ Then we establish a new characterization of holomorphic functions defined on open sets of ${\u2102}^{n}.$

We introduce the notion of (n,d)-sets and show several Noguchi-type convergence-extension theorems for (n,d)-sets.

A complex analytic space is said to have the D*-extension property if and only if any holomorphic map from the punctured disk to the given space extends to a holomorphic map from the whole disk to the same space. A Hartogs domain H over the base X (a complex space) is a subset of X x C where all the fibers over X are disks centered at the origin, possibly of infinite radius. Denote by φ the function giving the logarithm of the reciprocal of the radius of the fibers, so that, when X is pseudoconvex,...

In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Levi-flat “hat”. In our main theorem, we show that every ${\mathcal{C}}^{\infty}$-smooth CR diffeomorphism $h:M\to {M}^{\text{'}}$ between two globally minimal real analytic hypersurfaces in ${\u2102}^{n}$ ($n\ge 2$) is real analytic at every point...

If E is a closed subset of locally finite Hausdorff (2n-2)-measure on an n-dimensional complex manifold Ω and all the points of E are nonremovable for a meromorphic mapping of Ω E into a compact Kähler manifold, then E is a pure (n-1)-dimensional complex analytic subset of Ω.

We show that every closed subset of CN that has finite (2N - 2)-dimensional measure is a removable set for holomorphic functions, and we obtain a related result on the ball.