Browsing by Author "Vidras, Alekos"
Now showing items 117 of 17

Article
Analytic residues along algebraic cycles
Berenstein, Carlos A.; Vidras, Alekos; Yger, A. (2005)Let W be a qdimensional irreducible algebraic subvariety in the affine space A C n, P1,..., Pm m elements in C[X1,...,Xn], and V(P) the set of common zeros of the Pj's in C n. Assuming that W is not included in V(P), one ...

Article
Cauchy–Fantappiè Integral Formula for Holomorphic Functions on Special Tube Domains in $$\mathbb {C}^2$$C2
Alexandrou, N.; Vidras, Alekos (2019)

Article
ColeffHerrera Currents Revisited
Vidras, Alekos; Yger, A. (2012)In the present paper, we describe the recent approach to residue currents by Andersson, Björk, and Samuelsson (Andersson in Ann. Fac. Sci. ToulouseMath. Sér. 18(4):651661, 2009

Article
Division Theorems in Spaces of Entire Functions with Growth Conditions and their Applications to PDE of Infinite Order∗
Berenstein, Carlos A.; Berenstein, Carlos A.; Gay, R.; Vidras, Alekos; Vidras, Alekos (1994)It is shown that every entire function is “slowly decreasing”. As an application of this property, a theorem on analytic continuation of solutions of infinite order differential equations with constant coefficients is ...

Article
Duality for Hardy Spaces in Domains of ℂn and Some Applications
Aizenberg, L.; Gotlib, V.; Vidras, Alekos (2014)Let Ω ⊂ ℂn be a bounded, strictly convex domain with C3 boundary and Ω̃ be its dual complement. We prove that (Hp(Ω))″ = Hp(Ω̃), where p > 1 and 1/p + 1/q = 1. As an application of the above results we give the precise ...

Article
Geometric generalizations in KresinMaz'ya sharp realpart theorems
Aizenberg, L.; Vidras, Alekos (2008)In the present article we present some geometric generalizations of the estimates from Chapters 5,6,7 of the monograph [7]. © 2007 Birkhaeuser.

Article
Locally Explicit Fundamental Principle for Homogeneous Convolution Equations
Vidras, Alekos (2019)In the present paper a locally explicit version of Ehrenpreis's Fundamental Principle for a system of homogeneous convolution equations f · µj = 0, j = 1, ..., m, f ∈ E(Rn), µj ∈ E' (Rn), is derived, when the Fourier ...

Article
On a class of holomorphic functions representable by Carleman formulas in some class of bounded, simply connected domains from their values on an analytic arc
Chailos, George; Vidras, Alekos (2006)Let sript U sign be a bounded, simply connected domain with Jordan rectifiable boundary and let M ⊂ ∂ sript U sign be an open analytic arc whose Lebesgue measure satisfies 0 < m(M) < m(∂ sript U sign. Our result gives a ...

Article
On a class of holomorphic functions representable by Carleman formulas in the disk from their values on the arc of the circle
Aizenberg, L.; Vidras, Alekos (2007)Let D be a unit disk and M be an open arc of the unit circle whose Lebesgue measure satisfies 0 < l(M) < 2π Our first result characterizes the restriction of the holomorphic functions f ∈ H(D), which are in the Hardy class ...

Article
On a class of holomorphic functions representable by Carleman formulas in the interior of an equilateral cone from their values on its rigid base
Chailos, George; Vidras, Alekos (2005)Let Δ be an equilateral cone in C with vertices at the complex numbers 0, z10, z20 and rigid base M (Section 1). Assume that the positive real semiaxis is the bisectrix of the angle at the origin. For the base M of the ...

Article
On asymptotic approximations of the residual currents
Vidras, Alekos; Yger, A. (1998)We use a Pmodule approach to discuss positive examples for the existence of the unrestricted limit of the integrals involved in the approximation to the ColeffHerrera residual currents in the complete intersection case. ...

Article
On Carleman formulas and on the class of holomorphic functions representable by them
Aizenberg, L.; Vidras, Alekos (2002)Carleman formulas, unlike the Cauchy formula, restore a function holomorphic in a domain D by its values on a part M of the boundary ∂D, provided that M is of positive Lebesgue measure. An extensive survey of Carleman ...

Article
On holomorphic perturbations of infinite order differential equations
Vidras, Alekos (1997)It is proven in the present article that the solutions of infinite order differential equation with holomorphic parameter w ∈ U ⊂ ℂ depend holomorphically on w in the neighborhood of characteristic points of certain directions.

Article
On small complete sets of functions
Aizenberg, L.; Vidras, Alekos (2000)Using Local Residues and the Duality Principle a multidimensional variation of the completeness theorems by T. Carleman and A. F. Leontiev is proven for the space of holomorphic functions defined on a suitable open strip ...

Article
On some generalizations of Jacobi's residue formula
Vidras, Alekos; Yger, A. (2001)Using BochnerMartinelli type residual currents we prove some generalizations of Jacobi's residue formula, which allow proper polynomial maps to have 'common zeroes at infinity', in projective or toric situations. © 2001 ...

Article
On the Bohr radius for two classes of holomorphic functions
Aizenberg, L.; Vidras, Alekos (2004)Using some multidimensional analogs of the inequalities of E. Landau and F. Wiener for the Taylor coefficients of special classes of holomorphic functions on Reinhardt domains we obtain some estimates for the Bohr radius.

Article
Residue Currents and Bezout Identities
Berenstein, Carlos A.; Vidras, Alekos; Gay, Roger; Yger, Alain (1993)The objective of this monograph is to present a coherent picture of the almost mysterious role that analytic methods and, in particular, multidimensional residue have recently played in obtaining effective estimates for ...