Nikolaos D. Atreas

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The local behavior of regular wavelet sampling expansions is quantified. The term " regular " refers to the decay properties of scaling functions ϕ of a given multiresolu-tion analysis. The regularity of the sampling function corresponding to ϕ is proved. This regularity is used to determine small intervals of sampling points so that the sampled values of a(More)
The paper makes an attempt to introduce a new approach for detection of local singularities in signals, including one-dimensional time series and two-dimensional images. Inspired by a mode of antigen processing in the immune system, our approach is based on the rigorous mathematical methods of Discrete Tree Transform (DTT) and Singular Value Decomposition(More)
Let φ be a function in the Wiener amalgam space W∞(L 1) with a non-vanishing property in a neighborhood of the origin for its Fourier transform φ, τ = {τn} n∈Z be a sampling set on R and V τ φ be a closed subspace of L 2 (R) containing all linear combinations of τ-translates of φ. In this paper we prove that every function f ∈ V τ φ is uniquely determined(More)
Living in a rapidly changing world, where new threads emerge very often, security is in the epicentral of the international dialogue. Security is a broad term covering many activities like forecasting, prevention, building new communication and detection methodologies and many others., therefore many branches of science including mathematics has a lot to(More)
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