一类具有可积系数的四阶 J-对称微分算子的本质谱

摘要

By using the method of direct sum decomposition for operator and quadratic comparison ,the es-sential spectrum of a class of fourth-order J-symmetric differential operator with integrable coefficients is studied .T he existent range of essential spectrum and available scope of discrete spectrum are given .In addition ,the essential spectrum of a class of second-order J-symmetric differential operator with integra-ble coefficients to fourth-order is extended .At last ,a simple example about the essential spectrum of a class of fourth-order J-symmetric differential operator with integrable coefficients is given .%利用算子直和分解的方法和二次型比较的方法，研究了一类具有可积系数的四阶 J-对称微分算子的本质谱，得到了其本质谱的存在范围，并且给出了与之相对应的离散谱的存在范围。将具有可积系数的二阶 J-对称微分算子的本质谱推广到四阶，使其得到更广泛的应用。最后，对于这类具有可积系数的四阶 J-对称微分算子的本质谱提供了简明的实例。