Results in Q-measure

• Autorzy: Jisha C. R.

Identyfikatory

DOI

10.14708/ma.v50i2.7150

Warianty tytułu

PL

Wyniki związane z miarą Q

• Języki publikacji: EN

Abstrakty

EN

This paper introduces the notion of a generalized measure for a sequence of functions with oscillation and concentration effects. This measure is constructed by averaging the sequence of Borel measurable functions using singular or regular perturbations. In this way, the generalized limits of such sequences are conceptualized by enlarging the space of functions to measure spaces. It is a modification of the Young measure. This modified measure was termed a Q-measure. It can be difficult to determine the Young measure for a broad function. The Q-measure can be easily calculated for particular functions. This is one of the advantages of this study. As an application of the measure, we can define another weaker type of Monotone convergence theorem, the Lebesgue-dominated convergent theorem. A notion of average for underlying sequences to define the Q-measure is given, as also its application in signal analysis and atmospheric sciences.

PL

W tym artykule autor wprowadza nową miarę, którą nazywa miarą Q, reprezentującą słabą∗ granicę barycentrum ciągu funkcji borelowskich. Omawia niektóre wyniki zwi¡zane z tą miarą, co jest pomocne przy wyznaczaniu miary Q dla poszczególnych typów funkcji. Ponadto omówiono zastosowanie koncepcji średniej w analizie sygnałów i naukach o atmosferze.

Słowa kluczowe

EN

Young measure; atmospheric boundary layer; Borel measurable functions; Weak* limit; empirical mode decomposition

PL

nowa miara; funkcje borelowskie; słaba granica barycentrum; analiza sygnałów; funkcjonał Younga

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2022
• Tom: Vol. 50, no. 2
• Strony: 183--215
• Opis fizyczny: Bibliogr. 48 poz., rys., tab., wykr.

Twórcy

autor

Jisha C. R.

• SRM Institute of Science and Technology Research School, Chennai India 603203

• https://orcid.org/0000-0003-0319-2717

Bibliografia

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Uwagi

PL

Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023).