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.
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September 1994
Research Article|
September 01 1994
Space of test functions for higher‐order field theories
C. G. Bollini;
C. G. Bollini
Comisión de Investigaciones Científicas de la Provincia de Buenos Aires, Argentina
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L. E. Oxman;
L. E. Oxman
Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria 1428, Buenos Aires, Argentina
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M. Rocca
M. Rocca
Departamento de Física, Facultad de Ciencias Exactas, Universidad Nacional de La Plata, Argentina
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J. Math. Phys. 35, 4429–4438 (1994)
Article history
Received:
November 09 1993
Accepted:
April 20 1994
Citation
C. G. Bollini, L. E. Oxman, M. Rocca; Space of test functions for higher‐order field theories. J. Math. Phys. 1 September 1994; 35 (9): 4429–4438. https://doi.org/10.1063/1.530862
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