非齐次四阶薛定号算子谱测度的加权估计
Weighted Estimates for the Spectral Projection of Inhomogeneous Fourth-Order Schro¨dinger Operator in R2
摘要: 非齐次四阶薛定号算子 ∆2 − ∆ + V 在非线性光学中有着重要应用. 本文将在二维欧氏空间中建立算子的谱测度的加权估计. 此外，对算子的能量阁值 0 分三类：正则、共振、特征值进行讨论，给出共振和特征值对谱测度加权估计的影响。
Abstract: The inhomogeneous fourth-order Schrodinger operator ∆2 − ∆ + V has important applications in nonlinear optics. This paper establishes weighted estimates for the spectral measure of this operator in two-dimensional Euclidean space. Moreover, the energy threshold 0 is classified into three types: regular, resonance, and eigenvalue. We discuss the impact of resonances and eigenvalues on the weighted estimates of the spectral measure.
文章引用：李娅玲, 冯红亮. 非齐次四阶薛定号算子谱测度的加权估计[J]. 理论数学, 2026, 16(1): 146-164. https://doi.org/10.12677/PM.2026.161018

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