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- 42-XX Harmonic analysis on Euclidean spaces
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We propose a cryptographic algorithm utilizing integer wavelet transform via a lifting scheme. In this research, we construct some predict and update operators within the lifting scheme of wavelet transforms employing operations in min-max-plus algebra, termed as lifting scheme integer wavelet transform over min-max-plus algebra (MMPLS-IWavelet). The analysis and synthesis process on MMPLS-IWavelet is implemented for both encryption and decryption processes. The encryption key comprises a sequence...
The aim of this paper is to prove a quantitative version of Shapiro's uncertainty principle for orthonormal sequences in the setting of Gabor-Hankel theory.
Consider the linear congruence equation for , . Let denote the generalized gcd of and which is the largest with dividing and simultaneously. Let be all positive divisors of . For each , define . K. Bibak et al. (2016) gave a formula using Ramanujan sums for the number of solutions of the above congruence equation with some gcd restrictions on . We generalize their result with generalized gcd restrictions on and prove that for the above linear congruence, the number of solutions...
The object of this note is to generalize some Fourier inequalities.
The construction of nonseparable and compactly supported orthonormal wavelet bases of L 2(R n); n ≥ 2, is still a challenging and an open research problem. In this paper, we provide a special method for the construction of such wavelet bases. The wavelets constructed by this method are dyadic wavelets. Also, we show that our proposed method can be adapted for an eventual construction of multidimensional orthogonal multiwavelet matrix masks, candidates for generating multidimensional multiwavelet...
Let be a sequence of arbitrary complex numbers, let α,β > -1, let Pₙα,βn=0+∞
A generalized convolution with a weight function for the Fourier cosine
and sine transforms is introduced. Its properties and applications to solving
a system of integral equations are considered.
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