Search results for "Absolute"

A bilinear version of Orlicz–Pettis theorem

2008

Abstract Given three Banach spaces X, Y and Z and a bounded bilinear map B : X × Y → Z , a sequence x = ( x n ) n ⊆ X is called B -absolutely summable if ∑ n = 1 ∞ ‖ B ( x n , y ) ‖ Z is finite for any y ∈ Y . Connections of this space with l weak 1 ( X ) are presented. A sequence x = ( x n ) n ⊆ X is called B -unconditionally summable if ∑ n = 1 ∞ | 〈 B ( x n , y ) , z ∗ 〉 | is finite for any y ∈ Y and z ∗ ∈ Z ∗ and for any M ⊆ N there exists x M ∈ X for which ∑ n ∈ M 〈 B ( x n , y ) , z ∗ 〉 = 〈 B ( x M , y ) , z ∗ 〉 for all y ∈ Y and z ∗ ∈ Z ∗ . A bilinear version of Orlicz–Pettis theorem is given in this setting and some applications are presented.

Pilar Zambrano. PRINCÍPI, RAGIONI E DIRITTI. UN APPROCCIO AL DIRITTO COME DIFFERENZA PRATICA

2013

La costruzione 'con + DP + pseudorelativa': proposta per una duplice interpretazione

2015

This chapter deals with the so-called "absolute construction", an adverbial prepositional phrase headed by the preposition 'con' ('with') followed by a noun and a pseudo-relative clause (e.g. "Con Maria che piange, non possiamo uscire"). The main aim of the chapter is to show that Pseudo-relative clauses can have three different structures, and that two different types are used in the absolute construction, depending on the degree of syntactic integration of the prepositional phrase in the main clause. Fronted 'con'-clauses select a pseudo-relative clause with clausal status (CP), while sentence-final 'con'-clauses, which are more integrated, select a pseudo-relative clause with nominal sta…

Classes of regular Sobolev mappings

2008

We prove that a slight modification of the notion of α-absolute continuity introduced in [D. Bongiorno, Absolutely continuous functions in Rn, J. Math. Anal. Appl. 303 (2005) 119–134] is equivalent to the notion of n, λ-absolute continuity given by S. Hencl in [S. Hencl, On the notions of absolute continuity for functions of several variables, Fund. Math. 173 (2002) 175–189].

Comparison of the P-integral with Burkill's integrals and some applications to trigonometric series

2023

It is proved that the $P_r$-integral [9] which recovers a function from its derivative defined in the space $L^r$, 1 ≤r<∞, is properly included in Burkill’s trigonometric CP-and SCP-integrals. As an application to harmonic analysis, a de La Vallée-Poussin-type theorem for the $P_r$-integral is obtained: convergence nearly everywhere of a trigonometric series to a $P_r$-integrable function f implies that this series is the Pr-Fourier series of f.

THE HKr-INTEGRAL IS NOT CONTAINED IN THE Pr-INTEGRAL

2022

We compare a Perron-type integral with a Henstock-Kurzweiltype integral, both having been introduced to recover functions from their generalized derivatives defined in the metric Lr. We give an example of an HKr-integrable function which is not Pr-integrable, thereby showing that the first integral is strictly wider than the second one.

Regular subclasses in the Sobolev space W_{loc}^{1,n}

2009

Westudy some slight modifications of the class AC^n introduced in [D. Bongiorno, Absolutely continuous functions in Rn, J. Math. Anal. and Appl. 303 (2005) 119 134]. In particular we prove that the classes introduced in [C. Di Bari, C. Vetro, A remark on absolutely continuous functions in R^n, Rend. Circ. Matem. Palermo 55 (2006) 296 304] are independent by and contain properly the class AC^n.

Background studies for acoustic neutrino detection at the South Pole

2011

The detection of acoustic signals from ultra-high energy neutrino interactions is a promising method to measure the tiny flux of cosmogenic neutrinos expected on Earth. The energy threshold for this process depends strongly on the absolute noise level in the target material. The South Pole Acoustic Test Setup (SPATS), deployed in the upper part of four boreholes of the IceCube Neutrino Observatory, has monitored the noise in Antarctic ice at the geographic South Pole for more than two years down to 500 m depth. The noise is very stable and Gaussian distributed. Lacking an in-situ calibration up to now, laboratory measurements have been used to estimate the absolute noise level in the 10 to …

On the Hencl's notion of absolute continuity

2009

Abstract We prove that a slight modification of the notion of α-absolute continuity introduced in [D. Bongiorno, Absolutely continuous functions in R n , J. Math. Anal. Appl. 303 (2005) 119–134] is equivalent to the notion of n, λ-absolute continuity given by S. Hencl in [S. Hencl, On the notions of absolute continuity for functions of several variables, Fund. Math. 173 (2002) 175–189].

An Absolute Majority for the SPD as an Unintended Consequence? The Land Election in Rhineland-Palatinate 2006

2007

The state election of 2006 in Rheinland-Pfalz resulted in a (bare) majority of seats for the SPD, which allows the party to govern alone for the first time in the history of the state. The CDU, on the other hand, received slightly less than one-third of the vote, an all-time low in its former stronghold. This result was by and large determined by factors at the state level. Yet it had a considerable impact at the federal level: it signalled the end of a string of devastating losses for the SPD, enhanced the standing of minister president Kurt Beck (now the SPD's chairman), and brought to an end the last coalition between the SPD and the FDP. These repercussions notwithstanding, there is no …