Some remarks on vector-valued integration

Date

2002-02-01

Author

Kadets, Vladimir
Shumyatskiy, Boris
Shvidkoy, Roman
Zheltukhın, Kostyantyn
Tseytlin, Leonid

Metadata

Show full item record

Item Usage Stats

189
views

0
downloads

The paper continues the study of the notion of Riemann–Lebesgue integral, which was introduced before by two of the authors. The result about the convexity of the limit set of integral sums is generalized to the case of weakly-compactly generated spaces. The notion of Riemann–Lebesgue integral is used to introduce new classes of Banach spaces. The properties of these new spaces are studied.

Subject Keywords

Functional Analysis, Functional Analysis

URI

https://hdl.handle.net/11511/76330

Journal

Journal of Mathematical Physics, Analysis, Geometry

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Isomorphisms of l-Köthe spaces Karapınar, Erdal; Yurdakul, Murat Hayrettin; Department of Mathematics (2004) In this thesis, we study on l-Köthe spaces. By the help of interpolation theory, we use linear topological invariants to get isomorphisms of Cartesian products of l-power series spaces. We also see that multirectangular n-equivalent characteristics is linear toplogical invariant for power l-Köthe spaces of first type.
On the reduction principle for differential equations with piecewise constant argument of generalized type Akhmet, Marat (Elsevier BV, 2007-12-01) In this paper we introduce a new type of differential equations with piecewise constant argument (EPCAG), more general than EPCA [K.L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl. 99 (1984) 265-297; J. Wiener, Generalized Solutions of Functional Differential Equations, World Scientific, Singapore, 1993]. The Reduction Principle [V.A. Pliss, The reduction principle in the theory of the stability of motion, Izv. Akad. Nauk SSSR Ser. Mat. 27 (1964) 1297...
Integral manifolds of differential equations with piecewise constant argument of generalized type Akhmet, Marat (Elsevier BV, 2007-01-15) In this paper we introduce a general type of differential equations with piecewise constant argument (EPCAG). The existence of global integral manifolds of the quasilinear EPCAG is established when the associated linear homogeneous system has an exponential dichotomy. The smoothness of the manifolds is investigated. The existence of bounded and periodic solutions is considered. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Ap...
On the consistency of the solutions of the space fractional Schroumldinger equation (vol 53, 042105, 2012) Bayin, Selcuk S. (2012-08-01) Recently we have reanalyzed the consistency of the solutions of the space fractional Schroumldinger equation found in a piecewise manner, and showed that an exact and a proper treatment of the relevant integrals prove that they are consistent. In this comment, for clarity, we present additional information about the critical integrals and describe how their analytic continuation is accomplished.
Stability of differential equations with piecewise constant arguments of generalized type Akhmet, Marat (Elsevier BV, 2008-02-15) In this paper we continue to consider differential equations with piecewise constant argument of generalized type (EPCAG) [M.U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal. TMA 66 (2007) 367-383]. A deviating function of a new form is introduced. The linear and quasilinear systems are under discussion. The structure of the sets of solutions is specified. Necessary and Sufficient conditions for stability of the zero Solution are ob...

Citation Formats

V. Kadets, B. Shumyatskiy, R. Shvidkoy, K. Zheltukhın, and L. Tseytlin, “Some remarks on vector-valued integration,” Journal of Mathematical Physics, Analysis, Geometry, pp. 48–65, 2002, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/76330.