| title: | Methods of classical analysis and topological vector spaces in sequence spaces |
|---|---|
| reg no: | ETF5376 |
| project type: | Estonian Science Foundation research grant |
| subject: |
1.1-1.5. Exact Sciences |
| status: | accepted |
| institution: | TU Faculty of Mathematics |
| head of project: | Toivo Leiger |
| duration: | 01.01.2003 - 31.12.2006 |
| description: | The overall aim of the project is development of new methods by means of a synthesis of approaches of sequence spaces and summability theory, with a specific object of investigations of some presently significant problems: 1. Dual of the L_phi-space. We presume that we can endow the separable-FK-hull of a sequence space with topology that gives us the possibility to describe continuous linear functionals on L_phi-spaces. We will find out whether (a) FK-hull and A_phi-space and (b) summability-hull and summability domain type space enjoy similar connections between them. 2. General properties of SM-maps. We will continue investigations of new summability methods which have been started within ESF grant project 3991. We will apply the properties of these methods for descriptions of ordinary matrix methods. 3. Sequence spaces which enjoy Hahn properties. We will continue the investigations of these by description of Hahn properties (the investigation has been started within the ESF grant project 3991). We hope to produce an elucidation of relationships between these properties and find out which bounded summability domains have the Hahn property. We propose to describe modular spaces and their application to strong summability. For these investigations we need sequence space [c_A](F), its beta-dual and FK-envelope. 4. Knopp and Bonsall cores in sequence spaces. We will investigate the structure of sequence spaces determined by several cores by means of endowing these with natural topology for the core theory. 5. Convergence and summability with speed of orthogonal series. Investigation of the convergence and summability with speed for the series with Fourier-Walsh coefficients defined by multiplicative systems. |
| project group | ||||
|---|---|---|---|---|
| no | name | institution | position | |
| 1. | Toivo Leiger | TU Faculty of Mathematics | professor | |
| 2. | Leiki Loone | U. of Tartu | Assoc. Prof. | |
| 3. | Natalia Saealle | Tartu Ülikool | Ph.D. student | |
| 4. | Virge Soomer | U. of Tartu | Assoc. Prof. | |
| 5. | Maria Zeltser | U. of Tartu | Research Fellow | |