Convergenza in variazione e convergenza in lunghezza

Riassunto Viene stabilita, per le trasformazioni continue di una regione piana pluriconnessa, una maggiorazione per il numero delle imagini reciproche di un insieme dik punti del piano-imagine. Dalla disuguaglianza discende una limitazione superiore per il numero dei punti ?eccezionali?, ossia aventi un numero di modelli minore a quanti ne comporterebbe l'indice topologico.

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Résumé On établit, pour les transformations continues d'une région plane à plusieurs contours, une majoration du nombre des points de l'ensemble image-inverse d'un ensemble dek points du plane-image. Il en ressort une borne supérieure pour le nombre des points exceptionnels, c'e.-à-d. ayant moins d'images inverses qu'on s'attendrait de l'indice topologique.

     

Sulla convergenza in lunghezza delle medie integrali

Sunto Si fanno alcune considerazioni critiche sulla convergenza in lunghezza e in area di alcuni tipi di medie, mettendo in luce il carattere di passaggio al limite sotto il segno del classico teorema di Tonelli. A Giovanni Sansone nel suo 70^mo compleanno.     

Valor assoluto,variazione, lunghezza in distribuzione

a Enrico Bompiani in occasione del suo Giubileo scientifico. Lavoro eseguito nell' ambito del gruppo di rieerea N. 18 del C.N.R.     

Sul pendolo di lunghezza variabile

Rendiconti del Circolo Matematico di Palermo Series 1 -     

Sulla convergenza in categoria delle serie trigonometriche

Being evident (prop. 1) that the Fourier series of a function can be not convergent in cathegory (as defined in [4]) to the function itself, it is proved (Theorem 1) that for a continuous functionf there exist a trigonometric series having partial sums uniformily bounded and converging tof on a setX of second category. It is also proved (prop. 2) that, even renouncing to the uniform boundedness of partial sums, the setX cannot be chosen of full measure.     

P-convessità e convergenza di geodetiche

Summary We consider a sequence of energy functionals for regular paths with fixed extremes and whose range is contained in a corresponding sequence(M _h)_h∈Z+ of subsets of an Hilbert space. Assuming on eachM _h a condition similar top-convexity [C], we prove that if(M _h)_h∈Z+ is convergent in the sense of Kuratowsky toM the corresponding sequence(f _h)_h∈Z+of energy functionals is Γ-convergent to the functionalf relative toM and critical points off _h,i.e. the geodesics, are convergent to those off.      

Sulla convergenza delle serie reali a termini non negativi

In this paper some necessary and sufficient conditions are given for convergence of a series with non-negative terms. As a particular case, one finds again the well-known ratio-test for convergence of series with positive terms; in such a connection, some observations are made of didactical interest. Finally, some relations are emphasiged concerning theorems of convergence for real series (here obtained) and fixed point theorems already known.     

Sul metodo delle approssimazioni successive: Convergenza globale e plus-convergenza globale

With reference to the notions of global convergence and plus-global convergence introduced in [4], we prove that, for a dendriteX with a finite number of end points and a continuous mapF ofX into itself, the successive approximations method relative to pair (X, F) converges globally if and only ifF has no periodic points; furthermore, we show that ifF has no periodic points and the set of fixed points ofF is totally disconnected then the successive approximations method relative to the pair (X, F) plus-converge globally. Some auxiliary propositions have been proved in more general topological areas. One of them refers to a compact metric space (Γ,d′), to a continuous map ? of Γ into itself and to a sequence \((x_n )_{n \in IN} \) of points of Γ such that the sequence \((d^1 (x_{n + 1} ,\varphi (x_n )))_{n \in IN} \) converges to zero, and concerns the set of the cluster points of the sequence \((x_n )_{n \in IN} \) . In the end the global convergence and plus-global convergence in any metric space are characterized.     

Sui teoremi di convergenza delle medie nei processi non stazionari

Lavoro eseguito per la realizzazione del programma del gruppo di ricerca n. 20 del C.N.R. (1960–61).