共查询到18条相似文献,搜索用时 78 毫秒
1.
王红军赵佳 《应用泛函分析学报》2020,(4):207-218
本文研究了度量图上二阶及四阶局部微分算子积的自伴顶点条件.在研究闭区间[a,b]上积算子自伴性的基础上,运用度量图上高阶局部微分算子的自伴顶点条件得到了积算子自伴的充分必要条件.此外,给出了积算子自伴与原算子自伴之间的关系. 相似文献
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利用算子理论及矩阵运算方法,讨论了由两类不同的对称微分算式D~((4))+D~((2))+q_1(t)和D~((4))+q_2(t)(D=d/dt,t∈I=[a,b])生成的微分算子的积算子的自伴性,获得了积算子是自伴算子的充分必要条件. 相似文献
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利用矩阵运算及算子的基本理论,讨论了由微分算式L_1=D~((2))+q_1(t)和L_2=D~((4))+q_2(t)其中(D=d/dx,t∈I=[a,b])生成的两个微分算子L_i(i=1,2)积L_1L_2的自伴性问题,并在常型情形下,获得了积算子自伴的充分必要条件. 相似文献
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考虑[a,b](-∞<a<b<∞)上n阶复值系数正则对称微分算式ly=∑n j=0 aj(t)y(j).本文首先给出由lmy(m∈N且m≥2)生成的微分算子T(lm)自伴边条件一种新的描述,其次研究了由微分算式ly生成的m个微分算子Tk(l)(k=1,…,m)的积Tm(l)…T2(l)T1(l)的自伴性并获得其自伴的充分必要条件. 相似文献
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林秋红 《数学的实践与认识》2018,(3)
运用算子直和分解、Lidskii定理和二次型比较法,研究了一类具有对数函数系数的J-自伴微分算子谱的离散性,得到了这类J-自伴微分算子谱离散的若干充分条件. 相似文献
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本文在研究一类高阶微分算子谱的离散性的基础上研究了2n阶实系数Euler微分算式生成的对称微分算子,进一步完善了自伴Euler微分算子的谱是离散的充分必要条件. 相似文献
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In this paper, the problem of self-adjointness of the product of two differential operators is considered. A number of results
concerning self-adjointness of the productL
2
L
1 of two second-order self-adjoint differential operators are obtained by using the general construction theory of self-adjoint
extensions of ordinary differential operators.
Supported by the Royal Society and the National Natural Science Foundation of China and the Regional Science Foundation of
Inner Mongolia 相似文献
12.
J—自共轭微分算子谱的定性分析 总被引:6,自引:0,他引:6
本文对J-自共轭微分算子谱理论研究情况做一些概要性的介绍,第一部分简要回顾了J-自共轭微分算子理论研究的发展过程,第二,三部分介绍了J-自共轭微分算子的本质谱和离散谱定性分析的主要方法和结论;第四部分扼要叙述J-自共轭微分算子其它方面的一些工作,以及J-自共轭微分算子谱理论研究中尚待解决的问题。 相似文献
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In this paper, we present the definitions of generalized e-concave operators and generalized e-convex operators, which are the generalizations of e-concave operators and e-convex operators, respectively. Without compactness or continuity assumption of generalized e-concave operators and generalized e-convex operators, we have proved the existence, uniqueness and monotone iterative techniques of their fixed points. Our results are even new to e-concave operators and e-convex operators. Finally, we apply the results to the singular boundary value problems for second order differential equations. 相似文献
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In this paper, the product and commutativity of slant Toeplitz operators are discussed. We show that the product of kth1-order slant Toeplitz operators and kth2-order slant Toeplitz operators must be a (k1k2) th-order slant Toeplitz operator except for zero operators, and the commutativity and essential commutativity of two slant Toeplitz operators with different orders are the same. 相似文献
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Franç ois Germinet Abel Klein 《Proceedings of the American Mathematical Society》2003,131(3):911-920
We study the decay at large distances of operator kernels of functions of generalized Schrödinger operators, a class of semibounded second order partial differential operators of mathematical physics, which includes the Schrödinger operator, the magnetic Schrödinger operator, and the classical wave operators (i.e., acoustic operator, Maxwell operator, and other second order partial differential operators associated with classical wave equations). We derive an improved Combes-Thomas estimate, obtaining an explicit lower bound on the rate of exponential decay of the operator kernel of the resolvent. We prove that for slowly decreasing smooth functions the operator kernels decay faster than any polynomial.
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A class of pseudo-monotone operators and its applications in PDE 总被引:3,自引:0,他引:3
In this paper we give a criterion of pseudo-monotone operators by which a class of operators related to elliptic partial differential
equations is recognized as pseudo-monotone operators. Some applications in boundary value problems for elliptic equations
and obstacle problems are given.
Research supported by the Fund of IMAS 相似文献
18.
Young Joo Lee 《Journal of Mathematical Analysis and Applications》2007,329(2):1316-1329
We study some algebraic properties of Toeplitz operators on the Dirichlet space. We first characterize (semi-)commuting Toeplitz operators with harmonic symbols. Next we study the product problem of when product of two Toeplitz operators is another Toeplitz operator. As an application, we show that the zero product of two Toeplitz operators with harmonic symbol has only a trivial solution. Also, the corresponding compact product problem is studied. 相似文献