Uncertainty principles for continuous wavelet transforms related to the Riemann–Liouville operator
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DOI: 10.1007/s11587-017-0320-5
Abstract: In this paper we define and study the continuous wavelet transforms associated with the Riemann–Liouville operator, we give nice harmonic analysis results. Next we establish an analogue of Heisenberg’s inequality related to the wavelet transform.… read more here.
Keywords: continuous wavelet; liouville operator; wavelet transforms; wavelet ... See more keywords
A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph
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DOI: 10.1007/s13324-017-0172-x
Abstract: The Sturm–Liouville operator on a star-shaped graph is considered. We assume that the potential is known a priori on all the edges except one, and study the partial inverse problem, which consists in recovering the… read more here.
Keywords: sturm liouville; operator star; inverse problem; liouville operator ... See more keywords
Basis Properties in Lp of a Sturm-Liouville Operator with Spectral Parameter in the Boundary Conditions
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DOI: 10.1134/s0012266119020010
Abstract: The Sturm-Liouville operator with spectral parameter in the boundary conditions is considered, and sufficient conditions for the basis property of the system of eigenfunctions of this operator in the space Lp(0, 1), 1 < p… read more here.
Keywords: operator spectral; boundary conditions; parameter boundary; sturm liouville ... See more keywords
Classical Equiconvergence Problem for the Sturm-Liouville Operator with a Singular Potential
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DOI: 10.1134/s0012266119040062
Abstract: We study the classical problem of equiconvergence of spectral expansions for the Sturm-Liouville operator with a singular potential. We present various conditions on the potential guaranteeing the equiconvergence for the expansions of an arbitrary integrable… read more here.
Keywords: equiconvergence; problem; sturm liouville; operator singular ... See more keywords
Spectral properties of an impulsive Sturm–Liouville operator
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DOI: 10.1186/s13660-018-1781-0
Abstract: This work is devoted to discuss some spectral properties and the scattering function of the impulsive operator generated by the Sturm–Liouville equation. We present a different method to investigate the spectral singularities and eigenvalues of… read more here.
Keywords: sturm liouville; spectral properties; properties impulsive; impulsive sturm ... See more keywords
The formula for the regularized trace of the Sturm-Liouville operator with a logarithmic potential
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DOI: 10.5556/j.tkjm.50.2019.3354
Abstract: We have obtained a regularized trace formula for the Sturm-Liouville operator on a semi-axis with a logarithmic potential. read more here.
Keywords: sturm liouville; regularized trace; logarithmic potential; liouville operator ... See more keywords
Eigenvalue asymptotics for the Sturm-Liouville operator with potential having a strong local negative singularity
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DOI: 10.7494/opmath.2017.37.1.109
Abstract: We find asymptotic formulas for the eigenvalues of the Sturm-Liouville operator on the finite interval, with potential having a strong negative singularity at one endpoint. This is the case of limit circle in H. Weyl… read more here.
Keywords: sturm liouville; potential strong; negative singularity; liouville operator ... See more keywords