| title: | Integral (Fourier, Mellin) and matrix transformations for approximation of functions |
|---|---|
| reg no: | ETF5070 |
| project type: | Estonian Science Foundation research grant |
| subject: |
1.1. Mathematics |
| status: | completed |
| institution: | Tallinn University of Educational Sciences |
| head of project: | Andi Kivinukk |
| duration: | 01.01.2002 - 31.12.2005 |
| description: | 1. To investigate the problems of approximation of functions which have certain properties of symmetry by singular integrals of nonharmonic Fourier series ; to consider also the sampling series deduced by these nonharmonic Fourier series. 2. To investigate the possibilities for representation of functions by approximation methods of Mellin singular integral; to compare the orders of approximation of Fourier expansions by different means generated by continuous functions. 3. To apply the generalized Nörlund matrix and integral transformations and Abel- and Borel-type power series transformations to characterization of convergence of number and orthogonal series (comparatively for ordinary and strong summability); equivalence of these transformations for convergence of bounded sequences. 4. To investigate the Hausdorff summability methods defined by the Fredholm operator (called FH-methods). Obtained results could be: 1. - The estimations of norms of operators defined by singular integrals of nonharmonic Fourier series; - the degree of approximation by singular integrals using moduli of continuity; - the representations of functions by sampling series based on nonharmonic Fourier series. 2. - To deduce the necessary and sufficient conditions for representation of functions by transformed Mellin singular integral; to find corresponding orders of approximation; - to prove the comparison theorems and to find the order of approximation of means of Fourier expansions generated by continuous function. 3. - Theorems on ordinary and strong summabilities of number and orthogonal series by generalized Nörlund matrix and integral methods and Abel- and Borel-type methods; the estimates of rates of convergence and conditions for equivalence of these summability methods for bounded sequences. 4. The Tauberian and Mercerian theorems for FH-methods; applications to number and functional series. |
| project group | ||||
|---|---|---|---|---|
| no | name | institution | position | |
| 1. | Ants Aasma | Tallinn University of Educational Sciences | Assoc. Prof | |
| 2. | Andi Kivinukk | Tallinn Pedagogical University | Professor | |
| 3. | Olga Meronen | TPU, TTU | lab. assistant, doctoral student | |
| 4. | Veera Pavlova | TPU, Ulm University | research assistant | |
| 5. | Tamara Sõrmus | Tallinn University of Educational Sciences | retired, Research Ass. | |
| 6. | Anne Tali | Tallinn University of Educational Sciences | Assoc. Prof | |