Le Matematiche (Dipartimento di Matematica e Informatica, Università degli Studi di Catania)
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Approximation theorems for modified Szasz-Mirakjan operators in polynomial weight spaces
Get PDFIn this paper we will study properties of Szasz-Mirakjan type operators A_n^ν , B_n^ ν defined by modified Bessel function I_ν . We shall present theorems giving a degree of approximation for these operators
A covariant approach to symmetrizable and constrained hyperbolic systems
Get PDFA hyperbolic system with a convex extension is usually transformed in the symmetric form by taking the components of the main field as independent variables. However, the symmetric form can be obtained also in the original independent variables, which may have more physical meaning, by multiplying the system on the left by a suitable matrix P. Here the two methods are compared, showing also how to find the matrix P . The experience gained in this way, allows us to find also a new method to treat the systems with algebraic and differential constraints, without losing manifest covariance. The particular case of Lagrangian systems is also considered
Closed form representation of binomial sums and series
Get PDFThis paper deals with the classical quest for "closed form" expressions of binomial sums and series. We shall consider a generalised Binomial sum and some relations and investigate several methods for its representation in closed form. In the process of our analysis we shall "discover" several new identities and the closed form representation of a related series depending on a parameter
Uniqueness result for elliptic equations in unbounded domains
Get PDFFollowing the stream of ideas in two recent papers ([1], [8]), one can establish a uniqueness result for the Dirichlet problem for a class of elliptic second order differential equations with discontinuous coefficients in unbounded domains of R^n , n ≥ 3
On the equivalence of Phragmen-Lindelöf principles for holomorphic and plurisubharmonic functions
No full textThe existence of solutions of the Cauchy problem for (overdetermined) systems of linear partial differential operators with constant coefficients in some classes of functions or distributions is equivalent to the validity of Phragmen-Lindelöf-type principles ..
Hölder continuity of weak solutions to parabolic systems with controlled grouth non-linearities (two spatial dimensions)
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On some regularity and nonregularity results for solutions to parabolic systems
No full textA short survey of recent results on smoothness of weak solutions to parabolic systems with nonsmooth coefficients in olane is given. Moreover, for space dimensions n\ge 3 and any closed subset F in R^n we construct a linear parabolic system with bounded measurable coefficients and its solution which is essentially discontinuous on F and essentially continuous on R^n\F
The Stieltjes integral along fractal curve
Get PDFThe present paper is dealing with an integral over fractal non-rectifiable curve on the complex plane. In the introduction we observe its known indirect de�nitions. The Section 2 treats a direct definition, the existence theorems and some properties of the integral, and the next one concerns the Cauchy type integral along fractals. The final section consists of conjectures and open questions
Presentazione
No full textQuesto supplemento della rivista "Le Matematiche" è dedicato a Sergio Campanato, ..