By means of real analysis and weight functions, we obtain a few equivalent conditions of two kinds of Hardy-type integral inequalities with the non-homogeneous kernel and parameters. The constant factors related to the gamma function are proved to be the best possible. We also consider the operator expressions and some cases of homogeneous kernel.

We give a new Becchi-Rouet-Stora-Tyutin operator for the superstring. It implies a quadratic gauge-fixed action, and a new gauge-invariant action with first-class constraints. The infinite pyramid of spinor ghosts appears in a simple way through ghost gamma matrices. [email protected] and [email protected]

For a finitely generated discrete group $\Gamma$ acting properly on spin manifold $M$, we formulate new topological obstructions to $\Gamma$-invariant metrics of positive scalar curvature $M$ that take into account the cohomology classifying space $\underline{B}\Gamma$ for proper actions. In cocompact case, this leads natural generalisation Gromov-Lawson's notion higher $\hat{A}$-genera setting...

For certain Dirac operators $$\eth _{\phi }$$ associated to a fibered boundary metric $$g_{\phi , we provide pseudodifferential characterization of the limiting behavior $$(\eth }+k\gamma )^{-1}$$ as $$k\searrow 0$$ where $$\gamma $$ is self-adjoint operator anti-commuting with and whose square identity. This yields in particular low energy limit resolvent }^2$$ generalizing result Guillarmou S...

We prove that if $\Gamma$ is a group of polynomial growth, then each delocalized cyclic cocycle on the algebra has representative growth. For cocycle, we thus define higher analogue Lott’s eta invariant and its convergence for invertible differential operators. also use determinant map construction Xie Yu to there well-defined pairing between cocycles $K$-theory classes $C^\*$-algebraic seconda...

In this paper, we present new extensions of incomplete gamma, beta, Gauss hypergeometric, confluent hypergeometric function and Appell-Lauricella functions, by using the extended Bessel due to Boudjelkha [?]. Some recurrence relations, transformation formulas, Mellin transform integral representations are obtained for these generalizations. Further, an extension Riemann-Liouville fractional deri...

this paper presents characterizations of m-fuzzifying matroids bymeans of two kinds of fuzzy operators, called m-fuzzifying derived operatorsand m-fuzzifying difference derived operators.

we characterize compact composition operators on real banach spaces of complex-valued bounded lipschitz functions on metric spaces, not necessarily compact, with lipschitz involutions and determine their spectra.