Operators with memory in Schramm spaces

• Autorzy: Wróbel Małgorzata

Identyfikatory

DOI

10.17512/jamcm.2023.3.06

• Języki publikacji: EN

Abstrakty

EN

We show that every operator with memory acting between Banach spaces CΦBV(I) of continuous functions of bounded variation in the sense of Schramm defined on a compact interval I of a real axis, is a Nemytskij composition operator with the continuous generating function. Moreover, some consequences for uniformly bounded operators with memory will be given. As a by-product, we obtain that a Banach space CΦBV(I) has the uniform Matkowski property.

Słowa kluczowe

EN

operator with memory; locally defined operators; Nemytskij composition operator; Schramm type variation; continuous function; uniformly bounded operator

PL

operator Nemytskija; funkcja ciągła; przestrzeń Banacha

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2023
• Tom: Vol. 22, nr 3
• Strony: 69--80
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Wróbel Małgorzata

• Department of Mathematics, Czestochowa University of Technology, Czestochowa, Poland

Bibliografia

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• [2] Wróbel, M. (2010). Locally defined operators and a partial solution of a conjecture. Nonlinear Anal. TMA, 72, 495-506.
• [3] Wróbel, M. (2013). Locally defined operators in the space of functions of bounded ´ ϕ-variation. Real Anal. Exch., 38(1), 79-92.
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• [5] Schramm, M., & Waterman, D. (1982). Absolute convergence of Fourier series of functions of ΛBVp and ΦΛBV. Acta Math. Acad. Sci. Hung., 40(3-4), 273-276.
• [6] Brunner, H. (2017). Volterra Integral Equations. Cambridge University Press.
• [7] Kmit, I. (2021).C 1 -smoothness of Nemytskii operators on Sobolev-type spaces of periodic functions. Commentat. Math. Univ. Carol., 52(4), 507-517.
• [8] Grutzner, S., & Muntean, A. (2021). Identifying processes governing damage evolution in quasistatic elasticity, Part 1 - Analysis. Advances in Mathematical Sciences and Applications, 30(2), 305-334.
• [9] Krämer, R, & Mathé, P. (2008). Modulus of continuity of Nemytskii operators with application to the problem of option pricing. Journal of Inverse and III-posed Problems, 16(5), 435-461.
• [10] Appell, J., Banas, J., & Merentes, N. (2014). Bounded Variation and Around. Berlin, Boston: De Gruyter.
• [11] Guerrero, J.A, Leiva, H., Matkowski, J., & Merentes, N. (2010). Uniformly continuous composition operators in the space of bounded ϕ-variation functions. Nonlinear Anal., 72, 3119-3123.
• [12] Wróbel, M. (2023). Schramm spaces and composition operators. J. Appl. Math. Comput. Mech., 22(2), 87-98.
• [13] Matkowski, J. (2011). Uniformly bounded composition operators between general Lipschitz function normed spaces. Topol. Methods Nonlinear Anal., 38(2), 395-405

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).