Fourier coefficients and growth of harmonic functions
We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so that H is an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity in terms of its Fourier coefficients in case H is not entire. F...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1987-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000528 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849308551864909824 |
|---|---|
| author | A. fryant H. Shankar |
| author_facet | A. fryant H. Shankar |
| author_sort | A. fryant |
| collection | DOAJ |
| description | We consider Harmonic Functions, H of several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so that H is an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity
in terms of its Fourier coefficients in case H is not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth measures, both in case H is entire or non-entire. |
| format | Article |
| id | doaj-art-027cb417c0e14fa7937c002d975d1b22 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-027cb417c0e14fa7937c002d975d1b222025-08-20T03:54:25ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110344345210.1155/S0161171287000528Fourier coefficients and growth of harmonic functionsA. fryant0H. Shankar1Department of Mathematics, Utica College of Syracuse University, Utica 13502, New York, USADepartment of Mathematics, Ohio University, Athens 45701, Ohio, USAWe consider Harmonic Functions, H of several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so that H is an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity in terms of its Fourier coefficients in case H is not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth measures, both in case H is entire or non-entire.http://dx.doi.org/10.1155/S0161171287000528harmonic functionspherical harmonicsentire harmonic functionradius of harmonicityFourier coefficientsorder and type growth measuresLiouville's theorem. |
| spellingShingle | A. fryant H. Shankar Fourier coefficients and growth of harmonic functions International Journal of Mathematics and Mathematical Sciences harmonic function spherical harmonics entire harmonic function radius of harmonicity Fourier coefficients order and type growth measures Liouville's theorem. |
| title | Fourier coefficients and growth of harmonic functions |
| title_full | Fourier coefficients and growth of harmonic functions |
| title_fullStr | Fourier coefficients and growth of harmonic functions |
| title_full_unstemmed | Fourier coefficients and growth of harmonic functions |
| title_short | Fourier coefficients and growth of harmonic functions |
| title_sort | fourier coefficients and growth of harmonic functions |
| topic | harmonic function spherical harmonics entire harmonic function radius of harmonicity Fourier coefficients order and type growth measures Liouville's theorem. |
| url | http://dx.doi.org/10.1155/S0161171287000528 |
| work_keys_str_mv | AT afryant fouriercoefficientsandgrowthofharmonicfunctions AT hshankar fouriercoefficientsandgrowthofharmonicfunctions |