In this paper, we study the perturbation of spectra for 2 ×2 operator matrices such as Mx ={A0 XB） AC and Mz = （Az CB） on the Hilbert space H K and the sets……
The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytica...The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method.The derived results are very consistent with the actual solutions to the problems.A graphical representation has been done for the solution of the problems at various fractional-order derivatives.Moreover,the solution in series form has the desired rate of convergence and provides the closed-form solutions.It is noted that the procedure can be modified in other directions for fractional order problems.展开更多
The authors characterize the (U+K) orbits of a class essentially normal operators and prove that some essentially normal operators with connected spectrum are strongly irreducible after a small compact perturbation....The authors characterize the (U+K) orbits of a class essentially normal operators and prove that some essentially normal operators with connected spectrum are strongly irreducible after a small compact perturbation. This partially answers a question of Domigo A. Herrero.展开更多
In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, ...In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L1（[-a,a]×[-1,1]）（a〉0）.展开更多
Let н be a complex, separable, infinite dimensional Hilbert space, T ε（Ｈ）. （ｕ＋Ｋ）（T） denotes the （ｕ＋ｋ）-orbit of T, i.e., （ｕ＋ｋ）（T） = {R-1TR: R is invertible and of the form unitary plus compact}...Let н be a complex, separable, infinite dimensional Hilbert space, T ε（Ｈ）. （ｕ＋Ｋ）（T） denotes the （ｕ＋ｋ）-orbit of T, i.e., （ｕ＋ｋ）（T） = {R-1TR: R is invertible and of the form unitary plus compact}. Let be an analytic and simply connected Cauchy domain in C and n ε N. A（, n） denotes the class of operators, each of which satisfies （i） T is essentially normal; （ii） σ（T） =, ρF（T） ∩ σ（T） = ; （iii） ind （λ-T） = -n, nul （λ-T） = 0 （λ∈Ω ）. It is proved that given T1, T2 ε A（, n） and ε > 0, there exists a compact operator K with K <ε such that T1 +Kε （ｕ＋ｋ）（T2）. This result generalizes a result of P. S. Guinand and L. Marcoux [6,15]. Furthermore, the authors give a character of the norm closure of （ｕ＋Ｋ）（T）, and prove that for each T ε A（, n）, there exists a compact （SI） perturbation of T whose norm can be arbitrarily small.展开更多
It is known that small perturbations of a Fredholm operatorL have nulls of dimension not larger than dimN(L). In this paper for any given positive integer κ ? dimN(L) we prove that there is a perturbation ofL which h...It is known that small perturbations of a Fredholm operatorL have nulls of dimension not larger than dimN(L). In this paper for any given positive integer κ ? dimN(L) we prove that there is a perturbation ofL which has an exactly κ-dimensional null. Actually, our proof gives a construction of the perturbation. We further apply our result to concrete examples of differential equations with degenerate homoclinic orbits, showing how many independent homoclinic orbits can be bifurcated from a perturbation.展开更多
This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One ... This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.展开更多
In the present paper, we define the S-left and the S-right essential spectra of a linear operator and we study the stability of the S-essential spectra on a Banach space.
Depending on the geometry of the domain, one can define—at least—three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to...Depending on the geometry of the domain, one can define—at least—three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to a converging sequence of domains.展开更多
基金Supported by the National Natural Science Foundation of China(No.10962004)Tianyuan Fund for Mathematics(No.11126307)+2 种基金the National Natural Science Foundation of Inner Mongolia(No.2011MS0104, 2012MS0105)the Research Program of Science at Universities of Inner Mongolia Autonomous Region(No.NJZZ11011)Program of Higher-level Talents of Inner Mongolia University(No.Z20100116)
文摘In this paper, we study the perturbation of spectra for 2 ×2 operator matrices such as Mx ={A0 XB） AC and Mz = （Az CB） on the Hilbert space H K and the sets……
文摘The present work describes the fractional view analysis of Newell-Whitehead-Segal equations,using an innovative technique.The work is carried with the help of the Caputo operator of fractional derivative.The analytical solutions of some numerical examples are presented to confirm the reliability of the proposed method.The derived results are very consistent with the actual solutions to the problems.A graphical representation has been done for the solution of the problems at various fractional-order derivatives.Moreover,the solution in series form has the desired rate of convergence and provides the closed-form solutions.It is noted that the procedure can be modified in other directions for fractional order problems.
文摘The authors characterize the (U+K) orbits of a class essentially normal operators and prove that some essentially normal operators with connected spectrum are strongly irreducible after a small compact perturbation. This partially answers a question of Domigo A. Herrero.
文摘In this paper, we develop some operational calculus inspired from the Fredholm operator theory to investigate the S-essential spectra of the sum and the product of two operators acting on a Banach space. Furthermore, we apply the obtained results to determine the S-essential spectra of an integro-differential operator with abstract boundary conditions in L1（[-a,a]×[-1,1]）（a〉0）.
文摘Let н be a complex, separable, infinite dimensional Hilbert space, T ε（Ｈ）. （ｕ＋Ｋ）（T） denotes the （ｕ＋ｋ）-orbit of T, i.e., （ｕ＋ｋ）（T） = {R-1TR: R is invertible and of the form unitary plus compact}. Let be an analytic and simply connected Cauchy domain in C and n ε N. A（, n） denotes the class of operators, each of which satisfies （i） T is essentially normal; （ii） σ（T） =, ρF（T） ∩ σ（T） = ; （iii） ind （λ-T） = -n, nul （λ-T） = 0 （λ∈Ω ）. It is proved that given T1, T2 ε A（, n） and ε > 0, there exists a compact operator K with K <ε such that T1 +Kε （ｕ＋ｋ）（T2）. This result generalizes a result of P. S. Guinand and L. Marcoux [6,15]. Furthermore, the authors give a character of the norm closure of （ｕ＋Ｋ）（T）, and prove that for each T ε A（, n）, there exists a compact （SI） perturbation of T whose norm can be arbitrarily small.
基金This work was supported by the National Natural Science Foundation of China(Grant No.10171071)China MOE Research Grants TRAPOYT.
文摘It is known that small perturbations of a Fredholm operatorL have nulls of dimension not larger than dimN(L). In this paper for any given positive integer κ ? dimN(L) we prove that there is a perturbation ofL which has an exactly κ-dimensional null. Actually, our proof gives a construction of the perturbation. We further apply our result to concrete examples of differential equations with degenerate homoclinic orbits, showing how many independent homoclinic orbits can be bifurcated from a perturbation.
基金in part by the National Science Foundation under grant DMS-9971608in part by the Office of Naval Research under grant N00014-95-1-0793+1 种基金in part by the National Science Foundation under grant DMS-9971608in part by the National Science Foundation
文摘 This work is concerned with asymptotic properties of a class of parabolic systems arising from singularly perturbed diffusions. The underlying system has a fast varying component and a slowly changing component. One of the distinct features is that the fast varying diffusion is transient. Under such a setup, this paper presents an asymptotic analysis of the solutions of such parabolic equations. Asymptotic expansions of functional satisfying the parabolic system are obtained. Error bounds are derived.
文摘In the present paper, we define the S-left and the S-right essential spectra of a linear operator and we study the stability of the S-essential spectra on a Banach space.
基金supported by the ANR Project INFAMIE (Grant No. ANR-15-CE40001)
文摘Depending on the geometry of the domain, one can define—at least—three different Stokes operators with Dirichlet boundary conditions. We describe how the resolvents of these Stokes operators converge with respect to a converging sequence of domains.
