arXiv subjects

N. Lam

Publications and source records attributed to N. Lam.

2 recordsLinked to original sources

arXiv2021

Hardy's Identities and Inequalities on Cartan-Hadamard Manifolds

We study the Hardy identities and inequalities on Cartan-Hadamard manifolds using the notion of a Bessel pair. These Hardy identities offer significantly more information on the existence/nonexistence of the extremal functions of the Hardy inequalities. These Hardy inequalities are in the spirit of Brezis-V\'{a}zquez in the Euclidean spaces. As direct consequences, we establish several Hardy type inequalities that provide substantial improvements as well as simple understandings to many known Hardy inequalities and Hardy-Poincar\'{e}-Sobolev type inequalities on hyperbolic spaces in the literature.

math.AP↗

arXiv2003

Quasi-finite representations,free field realizations,and character formulae of Lie superalgebras of infinite rank

We classify the quasi-finite irreducible highest weight modules over the infinite rank Lie superalgebras $\hgltwo$, $\hC$ and $\hD$, and determine the necessary and sufficient conditions for quasi-finite irreducible highest weight modules to be unitarizable with respect to natural $\ast$-structures of the Lie superalgebras. The unitarizable irreducible modules are constructed in terms of Fock spaces of free quantum fields, and explicit formulae for their formal characters are also obtained by investigating Howe dualities between the infinite rank Lie superalgebras and classical Lie groups.

math.QA↗