We introduce a new concept of general $G$-$eta$-monotone operator generalizing the general $(H,eta)$-monotone operator cite{arvar2, arvar1}, general $H-$ monotone operator cite{xiahuang} in Banach spaces, and also generalizing $G$-$eta$-monotone operator cite{zhang}, $(A, eta)$-monotone operator cite{verma2}, $A$-monotone operator cite{verma0}, $(H, eta)$-monotone operator cite{fanghuang}...

We introduce a positive phase-space representation for fermions, using the most general possible multimode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase s...

Traditional open surgical techniques require a surgeon to assume a posture of leaning over the patient with a direct eye-to-hand perspective. As new minimally invasive and remote surgical procedures evolve, the surgeon is not required to maintain the same posture as in open techniques. While more ergonomic postures may be facilitated, some current remote systems have maintained surgeon configur...

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V . In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a C-extension of Swiss-cheese partial operad. We also give a tensor-categorical formulation and constructions of open-c...

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a C-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical construc...

We introduce the notions of open-closed field algebra and open-closed field algebra over a vertex operator algebra V. In the case that V satisfies certain finiteness and reductivity conditions, we show that an open-closed field algebra over V canonically gives an algebra over a C-extension of the Swiss-cheese partial operad. We also give a tensor categorical formulation and categorical construc...

where dA is the normalized area measure in D. The case where α = 0 is known as the (unweighted) Bergman space, often simply denoted by A2. Let φ be an analytic map from the open unit disk D into itself. The operator that takes the analytic map f to f ◦ φ is a composition operator and is denoted by Cφ . A natural generalization of a composition operator is an operator that takes f to ψ · f ◦ φ, ...

Abstract. We consider the fractional Laplacian −(−1)α/2 on an open subset in Rd with zero exterior condition. We establish sharp two-sided estimates for the heat kernel of such a Dirichlet fractional Laplacian inC1,1 open sets. This heat kernel is also the transition density of a rotationally symmetric α-stable process killed upon leaving a C1,1 open set. Our results are the first sharp twoside...