We study the integral equation related to the three and higher dimensional
superradiance problem. Collective radiation phenomena has attracted the attention
of many physicists and chemists since the pioneering work of R. H. Dicke in 1954.
We first consider the three-dimensional superradiance problem and find a differential
operator that commutes with the integral operator related to the problem. We
find all the eigenfunctions of the differential operator and obtain a complete set of
eigensolutions for the three-dimensional superradiance problem. Generalization of
the three-dimensional superradiance integral equation is provided. A commuting differential
operator is found for this generalized problem. For the three dimensional
superradiance problem, an alternative set of complete eigenfunctions is also provided.
The kernel for the superradiance problem when restricted to one-dimension is the
same as appeared in the works of Slepian, Landau and Pollak. The uniqueness of the
differential operator commuting with that kernel is indicated. Finally, a concentration
problem for the signals which are bandlimited in disjoint frequency-intervals is
considered. The problem is to determine which bandlimited signals lose the smallest
fraction of their energy when restricted in a given time interval. A numerical
algorithm for solution and convergence theorems are given. Orthogonality properties
of analytically extended eigenfunctions over L2(−∞,∞) are also proved. Numerical
computations are carried out in support of the theory.
| Identifer | oai:union.ndltd.org:tamu.edu/oai:repository.tamu.edu:1969.1/ETD-TAMU-2010-08-8312 |
| Date | 2010 August 1900 |
| Creators | Sen Gupta, Indranil |
| Contributors | Chen, Goong |
| Source Sets | Texas A and M University |
| Language | en_US |
| Detected Language | English |
| Type | thesis, text |
| Format | application/pdf |
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