An evaluation of powers of the negative spectrum of Schrödinger operator equation with a singularity at zero
نویسنده
چکیده
*Correspondence: [email protected] Department of Business Administration, Faculty of Business, Karabuk University, Karabuk, Turkey Abstract In this study, we investigate the discreteness and finiteness of the negative spectrum of the differential operator L in the Hilbert space L2(H, [0, ∞)), defined as Ly = – d 2y dx2 + A(A+I) x2 y – Q(x)y, under the boundary condition y(0) = 0. In the case when the negative spectrum is finite, we obtain an evaluation for the sums of powers of the absolute values of negative eigenvalues. The obtained result is applied to a class of equations of mathematical physics.
منابع مشابه
On inverse problem for singular Sturm-Liouville operator with discontinuity conditions
In this study, properties of spectral characteristic are investigated for singular Sturm-Liouville operators in the case where an eigen parameter not only appears in the differential equation but is also linearly contained in the jump conditions. Also Weyl function for considering operator has been defined and the theorems which related to uniqueness of solution of inverse proble...
متن کاملMeasure of non strict singularity of Schechter essential spectrum of two bounded operators and application
In this paper, we discuss the essential spectrum of sum of two bounded operators using measure of non strict singularity. Based on this new investigation, a problem of one-speed neutron transport operator is presented.
متن کاملCross Efficiency Evaluation with Negative Data in Selecting the Best of Portfolio Using OWA Operator Weights
The present study is an attempt toward evaluating the performance of portfolios and asset selectionusing cross-efficiency evaluation. Cross-efficiency evaluation is an effective way of ranking decisionmaking units (DMUs) in data envelopment analysis (DEA). Conventional DEA models assume nonnegativevalues for inputs and outputs. However, we know that unlike return and skewness, varianceis the on...
متن کاملCalculation of the triple and double cross sections in the proton-hydrogen impact at the ionization channel by removing singularity in the scattering amplitudes
In the present work, the triple and double cross sections of atomic hydrogen ionization in collision with the proton are calculated. The potential of the interaction is considered as a Coulombic; also, the first and second order Born approximations have been used. The singularity of the Green operator in the second order approximation has been removed for the analytical solution of the scatt...
متن کاملDispersive Estimates for Four Dimensional Schrödinger and Wave Equations with Obstructions at Zero Energy
We investigate L(R) → L∞(R4) dispersive estimates for the Schrödinger operator H = −∆ + V when there are obstructions, a resonance or an eigenvalue, at zero energy. In particular, we show that if there is a resonance or an eigenvalue at zero energy then there is a time dependent, finite rank operator Ft satisfying ‖Ft‖L1→L∞ . 1/ log t for t > 2 such that ‖ePac − Ft‖L1→L∞ . t , for t > 2. We als...
متن کامل