A LAPLACE INTEGRAL, THE T–Y–Z EXPANSION, AND BEREZIN'S TRANSFORM ON A KÄHLER MANIFOLD

2005 ◽  
Vol 02 (03) ◽  
pp. 359-371 ◽  
Author(s):  
ANDREA LOI
Keyword(s):  
Asymptotic Expansion ◽  
Complex Manifold ◽  
Lower Order ◽  
Differential Operators ◽  
Expansion Formula ◽  
Covariant Derivatives ◽  
Open Set ◽  
Type Integral ◽  
Lower Order Terms ◽  
Laplace Type

Let M be an n-dimensional complex manifold endowed with a C∞ Kähler metric g. We show that a certain Laplace-type integral ℒm(x), when x varies in a sufficiently small open set U ⊂ M, has an asymptotic expansion [Formula: see text], where Cr:C∞(U) → C∞(U) are smooth differential operators depending on the curvature of g and its covariant derivatives. As a consequence we furnish a different proof of Lu's theorem by computing the lower order terms of Tian–Yau–Zelditch expansion in terms of the operator Cj. Finally, we compute the differential operators Qj of the expansion Ber m(f) = Σr≥0m-rQr(f) of Berezin's transform in terms of the operators Cj.

scholarly journals Boundary estimates for solutions to operators of p-Laplace type with lower order terms

2011 ◽  
Vol 250 (1) ◽  
pp. 264-291 ◽  
Author(s):  
Benny Avelin ◽  
Niklas L.P. Lundström ◽  
Kaj Nyström
Keyword(s):  
Lower Order ◽  
Boundary Estimates ◽  
Lower Order Terms ◽  
Laplace Type

scholarly journals HEAT KERNEL ASYMPTOTICS OF OPERATORS WITH NON-LAPLACE PRINCIPAL PART

2001 ◽  
Vol 13 (07) ◽  
pp. 847-890 ◽  
Author(s):  
IVAN G. AVRAMIDI ◽  
THOMAS BRANSON
Keyword(s):  
Asymptotic Expansion ◽  
Heat Kernel ◽  
Principal Part ◽  
Vector Bundles ◽  
Compact Riemannian Manifold ◽  
Differential Operators ◽  
Leading Order ◽  
Partial Differential Operators ◽  
Heat Kernel Asymptotics ◽  
Laplace Type

We consider second-order elliptic partial differential operators acting on sections of vector bundles over a compact Riemannian manifold without boundary, working without the assumption of Laplace-like principal part -∇μ∇μ. Our objective is to obtain information on the asymptotic expansions of the corresponding resolvent and the heat kernel. The heat kernel and the Green's function are constructed explicitly in the leading order. The first two coefficients of the heat kernel asymptotic expansion are computed explicitly. A new semi-classical ansatz as well as the complete recursion system for the heat kernel of non-Laplace type operators is constructed. Some particular cases are studied in more detail.

scholarly journals Noncoercive quasilinear elliptic operators with singular lower order terms

2021 ◽  
Vol 60 (3) ◽  
Author(s):  
Fernando Farroni ◽  
Luigi Greco ◽  
Gioconda Moscariello ◽  
Gabriella Zecca
Keyword(s):  
Dirichlet Problem ◽  
Lower Order ◽  
Obstacle Problem ◽  
Differential Operators ◽  
Existence Of A Solution ◽  
Marcinkiewicz Spaces ◽  
Higher Integrability ◽  
Elliptic Differential Operators ◽  
Quasilinear Elliptic ◽  
Lower Order Terms

AbstractWe consider a family of quasilinear second order elliptic differential operators which are not coercive and are defined by functions in Marcinkiewicz spaces. We prove the existence of a solution to the corresponding Dirichlet problem. The associated obstacle problem is also solved. Finally, we show higher integrability of a solution to the Dirichlet problem when the datum is more regular.

scholarly journals Nonlinear evolution problems with singular coefficients in the lower order terms

2021 ◽  
Vol 28 (4) ◽  
Author(s):  
Fernando Farroni ◽  
Luigi Greco ◽  
Gioconda Moscariello ◽  
Gabriella Zecca
Keyword(s):  
Lower Order ◽  
Time Horizon ◽  
Existence Result ◽  
Nonlinear Evolution ◽  
Order Term ◽  
Time Behavior ◽  
Infinite Time ◽  
Singular Coefficient ◽  
Singular Coefficients ◽  
Lower Order Terms

AbstractWe consider a Cauchy–Dirichlet problem for a quasilinear second order parabolic equation with lower order term driven by a singular coefficient. We establish an existence result to such a problem and we describe the time behavior of the solution in the case of the infinite–time horizon.

scholarly journals Existence results for nonlinear degenerate elliptic equations with lower order terms

2020 ◽  
Vol 10 (1) ◽  
pp. 301-310
Author(s):  
Weilin Zou ◽  
Xinxin Li
Keyword(s):  
Lower Order ◽  
Elliptic Equations ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Regularity Of Solutions ◽  
Degenerate Elliptic Equations ◽  
Degenerate Elliptic ◽  
Initial Boundary Value ◽  
Lower Order Terms ◽  
Nonlinear Degenerate

Abstract In this paper, we prove the existence and regularity of solutions of the homogeneous Dirichlet initial-boundary value problem for a class of degenerate elliptic equations with lower order terms. The results we obtained here, extend some existing ones of [2, 9, 11] in some sense.

Zero correlation with lower-order terms for automorphic L-functions

2016 ◽  
Vol 12 (01) ◽  
pp. 27-55
Author(s):  
Timothy L. Gillespie ◽  
Yangbo Ye
Keyword(s):  
Lower Order ◽  
Product Formula ◽  
Cuspidal Representation ◽  
Zero Correlation ◽  
Lower Order Terms ◽  
Refined Version ◽  
Low Order

Let [Formula: see text] be a self-contragredient automorphic cuspidal representation of [Formula: see text] for [Formula: see text]. Using a refined version of the Selberg orthogonality, we recompute the [Formula: see text]-level correlation of high non-trivial zeros of the product [Formula: see text]. In the process, we are able to extract certain low-order terms which suggest the asymptotics of these statistics are not necessarily universal, but depend upon the conductors of the representations and hence the ramification properties of the local components coming from each [Formula: see text]. The computation of these lower-order terms is unconditional as long as all [Formula: see text].

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