论文标题
凯勒（Keller）和利布（Lieb-Thirring）的特征值估计值
Keller and Lieb-Thirring estimates of the eigenvalues in the gap of Dirac operators
论文作者
论文摘要
我们估计了具有质量的dirac操作员的差异，该差异是质量的最低特征值。这种约束是凯勒（Keller）估计的Schrödinger操作员的狄拉克操作员的对应者，这相当于Gagliardo-Nirenberg-Sobolev插值不平等。解决了规范的域，自我接合，最优性和临界值，而最佳电位由具有Kerr非线性的Dirac方程式给出。出现了一种新的临界结合，这是特征值可能在基本频谱中达到间隙底部的潜力的最小值。然后将凯勒估计值扩展到差距中特征值的lieb-thirite不平等。我们的大部分结果都是在Birman-Schinginger的重新印象中建立的。
We estimate the lowest eigenvalue in the gap of the essential spectrum of a Dirac operator with mass in terms of a Lebesgue norm of the potential. Such a bound is the counterpart for Dirac operators of the Keller estimates for the Schrödinger operator, which are equivalent to Gagliardo-Nirenberg-Sobolev interpolation inequalities. Domain, self-adjointness, optimality and critical values of the norms are addressed, while the optimal potential is given by a Dirac equation with a Kerr nonlinearity. A new critical bound appears, which is the smallest value of the norm of the potential for which eigenvalues may reach the bottom of the gap in the essential spectrum. The Keller estimate is then extended to a Lieb-Thirring inequality for the eigenvalues in the gap. Most of our result are established in the Birman-Schwinger reformulation.
