Space of test functions for higher-order field theories
The fundamental space ζ is defined as the set of entire analytic functions [test functions φ(z)], which are rapidly decreasing on the real axis. The variable z corresponds to the complex energy plane. The conjugate or dual space ζ′ is the set of continuous linear functionals (distributions) on ζ. Am...
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| Acceso en línea: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v35_n9_p4429_Bollini http://hdl.handle.net/20.500.12110/paper_00222488_v35_n9_p4429_Bollini |
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paper:paper_00222488_v35_n9_p4429_Bollini2023-06-08T14:48:10Z Space of test functions for higher-order field theories Oxman, Luis E. The fundamental space ζ is defined as the set of entire analytic functions [test functions φ(z)], which are rapidly decreasing on the real axis. The variable z corresponds to the complex energy plane. The conjugate or dual space ζ′ is the set of continuous linear functionals (distributions) on ζ. Among those distributions are the propagators, determined by the poles implied by the equations of motion and the contour of integration implied by the boundary conditions. All propagators can be represented as linear combinations of elementary (one pole) functionals. The algebra of convolution products is also determined. The Fourier transformed space ζ̃ contains test functions φ̃(x). These functions are extra-rapidly decreasing, so that the exponentially increasing solutions of higher-order equations are distributions on ζ̃. © 1994 American Institute of Physics. Fil:Oxman, L.E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 1994 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v35_n9_p4429_Bollini http://hdl.handle.net/20.500.12110/paper_00222488_v35_n9_p4429_Bollini |
| institution |
Universidad de Buenos Aires |
| institution_str |
I-28 |
| repository_str |
R-134 |
| collection |
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) |
| description |
The fundamental space ζ is defined as the set of entire analytic functions [test functions φ(z)], which are rapidly decreasing on the real axis. The variable z corresponds to the complex energy plane. The conjugate or dual space ζ′ is the set of continuous linear functionals (distributions) on ζ. Among those distributions are the propagators, determined by the poles implied by the equations of motion and the contour of integration implied by the boundary conditions. All propagators can be represented as linear combinations of elementary (one pole) functionals. The algebra of convolution products is also determined. The Fourier transformed space ζ̃ contains test functions φ̃(x). These functions are extra-rapidly decreasing, so that the exponentially increasing solutions of higher-order equations are distributions on ζ̃. © 1994 American Institute of Physics. |
| author |
Oxman, Luis E. |
| spellingShingle |
Oxman, Luis E. Space of test functions for higher-order field theories |
| author_facet |
Oxman, Luis E. |
| author_sort |
Oxman, Luis E. |
| title |
Space of test functions for higher-order field theories |
| title_short |
Space of test functions for higher-order field theories |
| title_full |
Space of test functions for higher-order field theories |
| title_fullStr |
Space of test functions for higher-order field theories |
| title_full_unstemmed |
Space of test functions for higher-order field theories |
| title_sort |
space of test functions for higher-order field theories |
| publishDate |
1994 |
| url |
https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00222488_v35_n9_p4429_Bollini http://hdl.handle.net/20.500.12110/paper_00222488_v35_n9_p4429_Bollini |
| work_keys_str_mv |
AT oxmanluise spaceoftestfunctionsforhigherorderfieldtheories |
| _version_ |
1768544442047791104 |