A generalisation to the hybrid Fourier transform and its application |
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Institution: | Physics and Applied Mathematics Unit Indian Statistical Institute 203, B.T. Road, Kolkata - 700 108, India;Department of Mathematics Indian Institute of Science Bangalore 560012, India |
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Abstract: | The hybrid Fourier transform, involving a linear combination of the cosine and sine functions as its kernel, is generalised for discontinuous but integrable functions, in the half-range comprising of the positive real axis. The present generalisation of the hybrid transform is observed to be useful in the area of two-dimensional wave problems involving a two-fluid region as opposed to the well-known hybrid transform, known as Havelock's expansion theorem, whose use is limited to the study of water wave problems involving only a single fluid medium. |
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