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Pure Mathematics 2026
非齐次四阶薛定号算子谱测度的加权估计
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Abstract:
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。
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.
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