The purpose of the present paper is to introduce a class $D_{Sigma ;delta }^{n}C_{0}(alpha )$ of bi-concave functions defined by Al-Oboudi differential operator. We find estimates on the Taylor-Maclaurin coefficients $leftvert a_{2}rightvert $ and $leftvert a_{3}rightvert$ for functions in this class. Several consequences of these results are also pointed out in the form of corollaries.

Recent work has shown that complex quantum field theory emerges as a statistical mechanical approximation to an underlying noncommutative operator dynamics based on a total trace action. In this dynamics, scale invariance of the trace action becomes the statement 0 = ReTrT μ μ , with Tμν the operator stress energy tensor, and with Tr the trace over the underlying Hilbert space. We show that thi...

The one-particle density matrix $$\gamma(x, y)$$ is one of the key objects in quantum-mechanical approximation schemes. self-adjoint operator $$\Gamma$$ with kernel trace class, but no sharp results on decay its eigenvalues were previously known. note presents asymptotic formula $$\lambda_k \sim (Ak)^{-8/3}$$ , $$A \ge 0$$ as $$k\to\infty$$ for $$\lambda_k$$ and describes main ideas proof.

Abstract This paper explores the long journey from projective tensor products of a pair Banach spaces, passing through definition nuclear operators still on realm products, to notion trace-class Hilbert space, and shows how why these concepts (nuclear operators, that is) agree in end.