123,219 research outputs found
MR2741185 Talvila, Erik The regulated primitive integral. Illinois J. Math. 53 (2009), no. 4, 1187–1219. (Reviewer: Luisa Di Piazza) 46G12 (26A39 46E15 46F10)
No full textTalvila Erik, The regulated primitive integral. Illinois J. Math. 53 (2009), no. 4, 1187–1219, 46Gxx (26A39 46Exx) MR 2 741 185
A descriptive definition of an integral is a definition which provides a ``description'' of the space of primitives. The derivatives in some sense of the primitives are the integrands.
In this paper the author introduces a descriptive method of integrating distributions: the regulated primitive integral.
The set \textbf{B}_R= \{F: [-\infty,\infty]
\rightarrow {\bf R}
\ \ | \mbox{ F {\it is regulated and left continuous on }}\\
\ \ {\bf R},
\ \ F(-\infty)=0, \ \ F(\infty)\in {\bf R}\} is the family of primitives.
The derivative here is in the sense of the distributions (i.e. a distributional or weak derivative). Then the integrable distributions are those distributions (in the Schwartz's sense) that are the distributional derivative of a function in .
The regulated primitive integral is a proper extension of the integral of distribution defined by L. Schwartz [Théorie des distributions. (French) Publications de l'Institut de Mathématique de l'Université de Strasbourg, No. IX-X. Hermann, Paris 1966 xiii+420, 46.40 (44.00), MR0209834 (35730)]. Moreover it is proved that the space of regulated integrable distributions is the completion of the space of signed Radon measures in the Alexiewicz norm, but it is not the completion in this norm of the Henstock-Kurzweil integrable functions. The functions of bounded variation constitute its dual space and also the space of multipliers. In the introduction a wide
panorama of descriptive and constructive integration methods is given.
Reviewed by (L. Di Piazza
Variational measures in the theory of integration
No full text{Variational measures in the theory of integration}
{Luisa Di Piazza}
{Palermo , Italy}
We will present here some results concerning the variational measures associated to a real valued function, or, in a more general setting, to a vector valued function. Roughly speaking, given a function defined on an interval of the real line it is possible to construct, using suitable families of intervals, a measure which carries information about . If is a real valued function, then the -finiteness of the measure implies the a.e. differentiability of , while the absolute continuity of the measure characterizes the functions which are Henstock-Kurzweil primitives. The situation becomes more complicate if we consider functions taking values in an infinite dimensional Banach space. If the Banach space has the Radon-Nikod\'{y}m property, then it is possible to obtain properties similar to those of the real case. But it is surprising that by means of the variational measures it is possible to characterize the Banach space having the Radon-Nikod\'{y}m property.
\begin{thebibliography}{99}
\bibitem{bds1} B. Bongiorno, L. Di Piazza and V. Skvortsov,
\textit{ A new full descriptive characterization of Denjoy-Perron
integral}, Real Analysis Exchange, {\bf 21} (1995/96), 256--263.
\bibitem{bdm} B. Bongiorno, L. Di Piazza and K. Musial,
\textit{ A characterization of the
Radon-Nikod\'{y}m property by finitely additive interval
functions}, Illinois Journal of Mathematics. Volume 53, Number 1 (2009), 87-99.
\bibitem{db} D. Bongiorno, \textit{ Stepanoff's theorem in separable Banach
spaces}, Comment. Math. Univ. Ca\-ro\-linae, {\bf 39} (1998),
323--335.
\bibitem{ldp1} L. Di Piazza, \textit{ Varational measures in the theory of the
integration in }, Czechos. Math. Jour. 51(126) (2001), no. 1,
95--110.
\bibitem{vm} V. Marraffa, \textit{
A descriptive characterization of the
variational Henstock integral}, Proceedings of the International
Mathematics Conference (Manila, 1998), Matimy\'{a}s Mat. {\bf 22}
(1999), no. 2, 73--84
MR2569913: Rodríguez, José. Some examples in vector integration. Bull. Aust. Math. Soc. 80 (2009), no. 3, 384–392. (Reviewer: Luisa Di Piazza),
No full textThe paper deals with some classical examples in vector integration due to Phillips, Hagler and Talagrand, revisited from the point of view of the Birkhoff and McShane integrals. More precisely, the author considers:
- Phillips' example of a Pettis integrable function f which is not Birkhoff integrable [R. S. Phillips, Trans. Amer. Math. Soc. 47 (1940), 114--145; MR0002707 (2,103c)]. It is proved here that f is universally McShane integrable.
- Hagler's example of a scalarly measurable l∞-valued function g which is not strongly measurable. The function g is proved to be universally Birkhoff integrable.
- Talagrand's example of a bounded Pettis integrable function φ having no conditional expectation [M. Talagrand, Mem. Amer. Math. Soc. 51 (1984), no. 307, ix+224 pp.; MR0756174 (86j:46042)]. Here the author shows that φ is also Birkhoff integrable, giving a negative answer to the question whether conditional expectations exist within the Birkhoff theory.
Some interesting open problems are also stated.
Reviewed by Luisa Di Piazz
MR2684422 Deville, Robert; Rodríguez, José Integration in Hilbert generated Banach spaces. Israel J. Math. 177 (2010), 285–306. (Reviewer: Luisa Di Piazza)
No full text2010), 285–306, 46Exx (46J10)
It is known that each McShane integrable function is also Pettis integrable, while the reverse implication in general is not true.
The equivalence of McShane and Pettis integrability depends on
the target Banach space X and has been proven: by R. A. Gordon [Illinois J. Math. 34 (1990), no. 3, 557–567, 26A42 (28B15 46G10 49Q15)], and by D. H. Fremlin and J. Mendoza [Illinois J. Math. 38 (1994), no. 1, 127–147, 46G10 (28B05)] if X is separable, by D. Preiss and the reviewer [Illinois J. Math. 47 (2003), no. 4, 1177–1187. 28B05 (26A39 26E25 46G10)] if X=c_0(\Gamma) (for any set
\Gamma) or X is super-reflexive, by the second author of the present paper [J. Math. Anal. Appl. 341 (2008), no. 1, 80–90, 46G10 (28B05 46B99 47B10)] if X=L^1(\nu) (for any probability measure
\nu).
Here the authors show that the McShane and Pettis integrability coincide for functions taking values in a subspace of a Hilbert generated Banach space. This result includes all previous known ones concerning the above mentioned equivalence.
The used approach relies heavily on some special properties of the Markushevich bases of those Banach spaces. They also give a ZFC example of a scalarly negligible function which is not McShane integrable.
Moreover they prove that, whenever the target Banach space is super-reflexive generated, the Birkhoff integrability lies strictly between Bochner and McShane integrability. Reviewed by L. Di Piazz
MR2481817 (2010e:46040): Haluška, Ján; Hutník, Ondrej On vector integral inequalities. Mediterr. J. Math. 6 (2009), no. 1, 105–124. (Reviewer: Luisa Di Piazza),
No full textI. Dobrakov in his papers [Czechoslovak Math. J. 40(115) (1990), no. 1, 8--24; MR1032359 (90k:46097); Czechoslovak Math. J. 40(115) (1990), no. 3, 424--440; MR1065022 (91g:46052)] developed a theory for integrating vector-valued functions with respect to operator-valued measures:
Let X and Y be two Banach spaces, Δ be a δ-ring of subsets of a nonempty set T, L(X,Y) be the space of all continuous operators L:X→Y, and m:Δ→L(X,Y) be an operator-valued measure σ-additive in the strong operator topology of L(X,Y). A measurable function f:T→X is said to be integrable in the sense of Dobrakov if there exists a sequence of simple functions fn:T→X, n∈N, converging m-a.e. to f and the integrals ∫.fndm are uniformly σ-additive measures on σ(Δ) (i.e. the σ-algebra generated by Δ). The integral of the function f on E∈σ(Δ) is defined by the equality ∫Efdm=limn→∞∫Efndm.
The first author, in the papers [Math. Slovaca 43 (1993), no. 2, 185--192; MR1274601 (95f:46069); Rev. Roumaine Math. Pures Appl. 38 (1993), no. 4, 327--337; MR1258045 (95g:28008); Czechoslovak Math. J. 47(122) (1997), no. 2, 205--219; MR1452416 (98h:46044)], has generalized the Dobrakov integration to the complete bornological locally convex topological vector spaces (C.B.L.C.S., for short), developing a new technique for C.B.L.C.S. and operator-valued measures. The main novelty of such a theory is that instead of the "classical'' objects such as a submeasure, a norm, a metric, etc., he needs to work with lattices of submeasures, norms, etc.
In the present paper the authors first give a brief development of this new integration theory in C.B.L.C.S. (see Section 2). In Section 3 some inequalities, which are important tools in this Dobrakov-type integration technique, are proved.
Reviewed by Luisa Di Piazz
Progetto di fattibilità tecnico economica per la riqualificazione architettonica impiantistica e commerciale del mercato di piazza Cavour
No full textLa piazza del mercato costituisce attualmente il limite nord della parte pedonalizzata di corso Cavour, e si trova nelle immediate prossimità dell’area pedonale di via del Prione, in posizione di cerniera tra il centro storico a sud-est e il Quartiere Umbertino a nord-ovest. Una peculiarità dell’area è rappresentata dal fatto che essa è attualmente una sorta di ibrido tra un mercato in sede propria e una piazza su cui si svolge il mercato, ossia tra un edificio con una caratterizzazione funzionale ben precisa e uno spazio pubblico aperto. Il progetto di riqualificazione dello spazio pubblico, quindi, si prefigge di caratterizzare in maniera chiara degli ambiti complementari, ma distinti: l’uno, al centro, lasciato libero e attrezzato come una vera piazza; gli altri, intorno, adibiti all’attività commerciale. Per l’ambito centrale è prevista la realizzazione di due piccoli edifici che delimitano lo spazio a nord e a sud; al loro interno sono previste attività di bar e ristorazione. Per quanto concerne il mercato, le coperture a onda vengono conservate; il nostro progetto, però, prevede su di esse un intervento di manutenzione straordinaria e di parziale trasformazione, nonché la realizzazione di box fissi e di chiusure perimetrali in tutti e quattro i padiglioni del mercato. I bordi esterni, quelli interni e le testate vengono trattati in modo diverso, a seconda dei differenti contesti con cui si relazionano
A novel approach to channel decorrelation for stereo acoustic echo cancellation based on missing fundamental theory
No full textABSTRACT
Decorrelation is a well known issue in the context of Stereophonic Acoustic Echo Cancellation: it is related to the problem of uniquely identifying each pair of room acoustic paths, due to high inter- channel coherence. In this paper, a novel approach to decorrelate a stereo signal based on the missing fundamental phenomenon is proposed. An adaptive algorithm is employed to track the behavior of one of the two channels, ensuring a continuous decorrelation without affecting the stereo quality. Several results are presented comparing our approach with Masked Noise injection method in terms of Magnitude Square Coherence, Itakura Saito measure and Convergence Speed of adaptive filters in order to confirm the validity of the proposed approach.
Il prodotto, pubblicato negli atti della conferenza annuale IEEE Acoustics Speech and Signal Processing (ICASSP) molto nota e stimata nell’ambito della teoria dei circuiti a tempo discreto (DSP), contiene una proposta innovativa per la realizzazione di circuiti per la decorrelazione audio con particolare riferimento all’applicazione alla cancellazione d’eco in sistemi multicanale.
Il lavoro è stato successivamente pubblicato in [1] ed è alla base anche delle ulteriori pubblicazioni [2] e [3].
[1] Cecchi, S.; Romoli, L.; Peretti, P.; Piazza, F., “A Combined Psychoacoustic Approach for Stereo Acoustic Echo Cancellation”, IEEE Transaction on Audio, Speech, and Language processing, Vol. 19, no. 6, Aug 2011, Pages: 1530-1539.
[2] Cecchi, S.; Romoli, L.; Peretti, P.; Piazza, F., “A Mixed Decorrelation Approach for Stereo Acoustic Echo Cancellation Based on the Estimation of the Fundamental Frequency ”, IEEE Transaction on Audio, Speech, and Language processing, Vol. 20, no. 2, Feb 2012, Pages: 690-698.
[3] Cecchi, S.; Romoli, L.; Peretti, P.; Piazza, F., “Low-complexity implementation of a real-time decorrelation algorithm for stereophonic acoustic echo cancellation”, in pubblicazione su Signal Processing, editore Elsevier (già disponibile on-line sul sito dell’editore)
MR3058477 Reviewed Ereú, Thomás; Sánchez, José L.; Merentes, Nelson; Wróbel, Małgorzata Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Schramm. Pr. Nauk. Akad. Jana Długosza Częst. Mat. 16 (2011), 23–32. ISBN: 978-83-7455-209-7
No full textIn this paper it is established a property of a composition operator
between spaces of functions of bounded variation in the sense of Schramm.
Let X and Y be two real normed spaces, C a convex cone in X and
I a closed bounded interval of the real line. Moreover let cc(Y) be
the family of all non-empty closed convex and compact subsets of Y. The
authors study the Nemytskij (composition) operator (HF)(t)=h(t,F(t)),
where
F: I \rightarrow C and h: I\times C \rightarrow cc(Y) is a given
set-valued function. They show that if the Nemytskij operator is
uniformly continuous and maps the space \Phi BV (I;C) of functions
(from I to C) of bounded \Phi-variation in the sense of Schramm
into the space of set-valued functions (from I to
cc(Y)) of bounded \Psi-variation in the sense of Schramm, then the
one-sided regularizations h^- and h^+ of h with respect the first
variable are affine with respect to the second variable. Reviewed by ( L. Di Piazza
L'altra politica. la partecipazione tra movimenti sociali e attivismo civico nei vecchi e nuovi conflitti
No full textNella società contemporanea, scossa da un accelerato processo di mutamento sociale e politico che investe tanto le variabili strutturali quanto le condizioni soggettive della vita sociale, esiste un’ampia varietà di azioni e di pratiche che hanno una profonda valenza politica, ma che mal si prestano a essere spiegate utilizzando categorie e concetti con cui siamo abituati ad analizzare la politica stessa. Questo volume offre un quadro quanto mai articolato e aggiornato di tali esperienze, che prendono forma fuori dai confini della sfera delle istituzioni della democrazia rappresentativa, dunque nello spazio dell’altra politica. Dalle nuove lotte per il lavoro alle trasformazioni dei movimenti sociali, dalle forme della partecipazione cosiddetta “civile” fino agli ambiti raramente considerati dalla manualistica tradizionale come il tifo organizzato e le mobilitazioni dei migranti che lavorano come braccianti agricoli, i capitoli che compongono il manuale restituiscono uno sguardo d’insieme, supportato sia da solide chiavi di lettura teoriche e analitiche sia da esperienze e pratiche estremamente attuali. Per questi motivi, il testo si rivolge a un’ampia platea di studentesse e studenti, ricercatrici e ricercatori nonché cittadini, interessati a comprendere il complesso intreccio tra mutamento sociale e politico
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