7 citations · 17 across the 11 of their papers we have counts for
11 papers
Borg-type theorem for a class of higher-order differential operators
Ai-Wei Guan, Dong-Jie Wu, Chuan-Fu Yang +1
In this paper, we study an inverse spectral operator for the higher-order differential equation , where . We prove that if is su…
Borg-type theorem for a class of fourth-order differential operators
Ai-Wei Guan, Chuan-Fu Yang, Natalia P. Bondarenko
In this paper, we study an inverse spectral problem for the fourth-order differential equation with real-valued coefficients and of $L^2(0,1)…
A class of higher order inverse spectral problems
Ai-Wei Guan, Chuan-Fu Yang, Natalia P. Bondarenko
In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, wh…
Operations on the de Rham cohomology of Poisson and Jacobi manifolds
Ai Guan, Fernando Muro
We prove that the (homotopy) hypercommutative algebra structure on the de Rham cohomology of a Poisson or Jacobi manifold defined by several authors is (homotopically) trivial, i.e…
Hochschild cohomology of the second kind: Koszul duality and Morita invariance
Ai Guan, Julian Holstein, Andrey Lazarev +1
We define Hochschild cohomology of the second kind for differential graded (dg) or curved algebras as a derived functor in the twisted derived category. The Hochschild cohomology o…
Solving Barcilon's inverse problems by the method of spectral mappings
Aiwei Guan, Chuanfu Yang, Natalia P. Bondarenko
In this paper, we consider Barcilon's inverse problem, which consists of the recovery of the fourth-order differential operator from three spectra. We obtain the relationship of Ba…
Model category structures on multicomplexes
Xin Fu, Ai Guan, Muriel Livernet +1
We present a family of model structures on the category of multicomplexes. There is a cofibrantly generated model structure in which the weak equivalences are the morphisms inducin…
Review of deformation theory II: a homotopical approach
Ai Guan, Andrey Lazarev, Yunhe Sheng +1
We give a general treatment of deformation theory from the point of view of homotopical algebra following Hinich, Manetti and Pridham. In particular, we show that any deformation f…
Review of deformation theory I: Concrete formulas for deformations of algebraic structures
Ai Guan, Andrey Lazarev, Yunhe Sheng +1
In this review article, first we give the concrete formulas of representations and cohomologies of associative algebras, Lie algebras, pre-Lie algebras, Leibniz algebras and 3-Lie…
Koszul duality for compactly generated derived categories of second kind
Ai Guan, Andrey Lazarev
For any dg algebra we construct a closed model category structure on dg -modules such that the corresponding homotopy category is compactly generated by dg -modules that…
Gauge equivalence for complete -algebras
Ai Guan
We introduce a notion of left homotopy for Maurer--Cartan elements in -algebras and -algebras, and show that it corresponds to gauge equivalence in the diff…