in this paper, we introduce new classes $sum_{k,p,n}(alpha ,m,lambda ,l,rho )$ and $mathcal{t}_{k,p,n}(alpha ,m,lambda ,l,rho )$ of p-valent meromorphic functions defined by using the extended multiplier transformation operator. we use a strong convolution technique and derive inclusion results. a radius problem and some other interesting properties of these classes are discussed.

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

The localization of the essential spectrum of a relativistic twoelectron ion is provided. The analysis is performed with the help of the pseudorelativistic Brown-Ravenhall operator which is the restriction of the CoulombDirac operator to the electrons’ positive spectral subspace.

We consider the link average of the half-BPS Wilson loop operators in N = 6 superconformal Chern-Simons-matter theory, which is called ABJM theory. We show that this loop average is reduced to a (super)matrix integral by the localization method, in a similar way to the bosonic U(N) Chern-Simons theory. Using this matrix integral, we compute the twoand three-link averages with an operator formal...

We use Brownian motion ideas to study Schriidinger operators H = +A + V on Lp(R”). In particular: (a) We prove that limt+m t-l In /I e&H j111.9 is p-independent for a very large class of V’s where 11 A ll,,,n = norm of A as an operator from L’ to L”. (b) For Y > 3 and V E LY/~--E n L”Ip+c, we show that sup jl eetH Ilm,m -: (D if and only if H has no negative eigenvalues or zero energy resonance...

This paper establishes dynamical localization properties of certain families of unitary random operators on the d-dimensional lattice in various regimes. These operators are generalizations of one-dimensional physical models of quantum transport and draw their name from the analogy with the discrete Anderson model of solid state physics. They consist in a product of a deterministic unitary oper...