On a finite asymptotic integral transform
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Nassar H. S. Haidar
Abstract
We report on solving the inverse problem of finding the kernel of an asymptotic singular integral operator under which monomial signals that are compactly supported over the closed unit interval [0, 1–] are asymptotic generalized fixed points over the semi-closed unit interval (0, 1]. This operator defines a certain Even-Hilbert Riemann–Lebesgue transformation with a kernel that is double parameterized over a certain momentum Hilbert space. The inversion of this singular transformation is proved to be in the form of an associated Odd-Hilbert Riemann–Lebesgue transformation. The paper contains also proofs for a number of operational properties of this transform, with an identified area for potential applicability in solving certain functional initial-value problems.
© de Gruyter 2011
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- Inverse problem and null-controllability for parabolic systems
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- A generalization of continuous regularized Gauss–Newton method for ill-posed problems
- Direct and inverse problems of the theory of wave propagation in an elastic inhomogeneous medium
- Determination of the unknown time dependent coefficient p(t) in the parabolic equation ut = Δu + p(t)u + φ(x, t)
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- International Conference “Inverse and Ill-Posed Problems of Mathematical Physics” dedicated to the 80th birthday of Academician M. M. Lavrentiev
- The Sixth International Conference “Inverse Problems: Modeling & Simulation”
- Third International Scientific Conference and Young Scientists School “Theory and Computational Methods for Inverse and Ill-Posed Problems”
