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On Analytic Continuation, Multiplication, and Fourier Transformations of Schwartz Distributions
Journal of Mathematical Physics, 1961It is shown that a class of Schwartz distributions on the real axis can be continued to holomorphic functions in the upper and lower complex half-planes such that the ``jump'' on the real axis represents the distribution. Many operations with distributions can be reduced to operations with the associated holomorphic functions which is of particular ...
Bremermann, H. J., Durand, L.
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Multiple imaging and multiple Fourier transformation using planar microlens arrays
Applied Optics, 1990A new type of multiple imaging and multiple Fourier transformation system under coherent illumination using microlens arrays has been developed. The optical system is based on geometrical optics instead of convolution or diffraction. As a result, it has the advantage of design flexibility especially in alignment of the duplicate images.
K, Hamanaka +4 more
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Uniform convergence and integrability of multiplicative Fourier transforms
Mathematical Notes, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Volosivets, S. S., Golubov, B. I.
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Multiple order spectra in Fourier transform infrared spectroscopy
Applied Optics, 1977A phenomenon akin to higher order spectra in grating spectroscopy has been found in Fourier transform spectroscopy. While its relative intensity is orders of magnitude down from similar effects in gratings, the high sensitivity of Fourier transform ir allows this perturbation to be detected.
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Multiple imaging by lensless Fourier transform holography
Journal of Optics, 1979A simple method for producing multiple images is reported by recording a lensless Fourier transform hologram of the master object using a holographic grating. Relations for optimizing reference-to-object beam intensity ratio are derived in order to retain linearity and efficiency of the hologram.
P C Mehta, C Bhan, R Hradaynath
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The fast fourier transform in a problem with multiple grid-points
USSR Computational Mathematics and Mathematical Physics, 1988See the review in Zbl 0653.65098.
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Multiple Imaging and Multiple Fourier Transformation Using Microlens Arrays
Japanese Journal of Applied Physics, 1990A new type of coherent multiple imaging system using microlens arrays has been developed. The principles, features, basic functions and possible applications are also discussed with some experimental results which are implemented by using a planar microlens array fabricated by an ion exchange technique.
Kenjiro Hamanaka, Takashi Kishimoto
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Multiplicative Complexity of Discrete Fourier Transform
1988In this chapter the multiplicative complexity of the discrete Fourier transform (DFT) is analyzed. The next several sections define the DFT and then show how the complexity of the DFT is determined when the number of inputs is prime, a power of an odd prime, a power of two, and finally for any positive integer.
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On fast multiplication of polynomials, the Fourier and Hartley transforms
Discrete Mathematics and Applications, 2000Summary: We give a fast algorithm for multiplication of polynomials with real-valued coefficients without resort to complex numbers and the fast Fourier transformation. The efficiency of this algorithm is compared with the multiplication algorithm based on the discrete Hartley transformation.
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Multiple Fourier transform method on an SIMD computer
1995We implement a block tridiagonal Toeplitz linear system solver called MFT on an SIMD massively parallel computer, the MasPar MP-2. MP-2 is suitable to the linear solver which has rich data-parallelism. We examine five implementation methods to identify actual problems that hamper high-performance computing.
Hyoung Joong Kim +2 more
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