Fausto Segala

New results on the Pompeiu problem

Let PN(W) ENkO a w , w E C, N E N, be a polynomial with complex coefficients. In this paper we prove that if DC c2 is a simplyconnected bounded open set whose boundary is a closed, simple curve parametrized by x(s) = xl(s) + ix2(s) = pN(eLs), s E [-Xt, 7t], then D has the Pompeiu property unless N = 1 and p1 (w) = a1w + a2 in which case D is a disk. This result supports the conjecture that modulo sets of zero twodimensional Lebesgue measure, the disk is the only simply-connected, bounded open set which fails to have the Pompeiu property.

Univalent functions and the Pompeiu problem

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Parametrices for a class of differential operators with multiple characteristics

SummaryIn this paper we give the construction of a parametrix for a class of differential operators of the type ∂2/∂t2−t2k+1Δ + tq(∂/∂xi), k εN, q εN, q⩾k.

Convergence of a quadrature formula for the approximation of stress intensity factor for planar cracks

Recently we have presented a numerical quadrature formula for the evaluation of the stress intensity factor for convex planar cracks, given as integral approximation [Int. J. Numer. Methods Eng. 54 (2002) 241]. In this paper we prove convergence of this quadrature formula together with other theoretical estimates on the integral approximation.

Branch points, Fourier integrals and Pompeiu problem

SuntoSi prova che sep è un polinomio e la mappa

Another step toward the solution of the Pompeiu problem in the plane

h(w) = \sqrt {p(w)}

Propagation and reflection of singularities for a class of evolution equations

è univalente sul disco unitarioD del piano complesso, allora Ω=h(D) ha la proprietà di Pompeiu.AbstractLeth be the square root of a polynomial and assume thath is univalent on the unitary disk of the complex plane. Then the set Ω=h(D) has the Pompeiu property.