Integrable $\lambda$-deformed $\sigma$-models are characterized by an underlying current algebra/coset model CFT deformed, at the infinitesimal level, current/parafermion bilinears. We promote deformation parameters to dynamical functions of time introduced as extra coordinate. It is conceivable that appropriately constraining them, beta-functions vanish and consequently $\sigma$-model stays co...

Let X be a compact group. $(X) denotes the Banach algebra (point multiplication, sup norm) of continuous complexvalued functions on X A is any closed subalgebra of d(X) which is stable under right and left translations and contains the constants. It is shown, by means of the Peter-Weyl Theorem and some multilinear algebra, that the condition (*) every representation of degree 1 of X has finite ...

In [5], Lehmann gave a simple proof of this identity and used it in his study of some concepts of dependence. This identity was generalized to functions h(X) and g(Y) with E[h2(X)] <∞ and E[g2(Y)] <∞ and with finite derivatives h′(·) and g′(·) by Newman [6]. Multidimensional versions of these results were proved by Block and Fang [1], Yu [13], and more recently by Prakasa Rao [7]. Related covar...

and the norm of an element is defined by ||/|| = ƒ | f(t) \ dt. In [4] Rudin showed that every function in L(R) is the convolution of two other functions. In other words, every element of the convolution algebra L(R) can be factored in L 1 ^ )» although this algebra lacks a unit. Subsequently, Cohen [ l ] observed that the essential ingredient in Rudin's argument is that ^(R) has an approximate...

We mainly study the growth and Gelfand-Kirillov dimension (GK-dimension) of generalized Weyl algebra (GWA) $A=D(\sigma,a)$ where $D$ is a polynomial or Laurent algebra. Several necessary sufficient conditions for $\operatorname{GKdim}(A)=\operatorname{GKdim}(D)+1$ are given. In particular, we prove dichotomy GK-dimension GWAs over in two indeterminates, namely, $\operatorname{GKdim}(A)$ either ...

We establish the long time existence of complete non-compact weakly convex and smooth hypersurfaces $$\Sigma _t$$ evolving by $$Q_k$$ -flow. show that maximum T depends on dimension $$d_W$$ vector space $$W{:}{=}\{w \in \mathbb {R}^{n+1}: \sup _{X\in \Sigma _0} |\langle X,w\rangle | = +\infty \}$$ which contains each direction in our initial data _0$$ is infinite. If $$d_W=\text {dim}(W) \ge n-...

We study $$(\sigma ,\tau )$$ -derivations of a group ring RG where G is with center having finite index in and R semiprime 1 such that either has no torsion elements or if p-torsion elements, then p does not divide the order let $$\sigma $$ be R-linear endomorphisms fixing pointwise. generalize Main Theorem 1.1 Chaudhuri (Comm Algebra 47(9): 3800–3807, 2019) prove there $$T\supset R$$ $$\mat...

We study the range transformations 0p(/fD, Reß) and Op(/fD, B) for Banach function algebras A and B. As a special instance, the harmonicity of functions in Op(/fD, Re A) for a nontrivial function algebra A is established and is compared with previous investigations of Op( An, A) and Op((Re/l);, (Re/1)) for an interval /. In §2 we present some results on Op(AD, B) and use them to show that funct...

We show that the four-dimensional Chern-Simons theory studied by Costello, Witten and Yamazaki, is, with Nahm pole-type boundary conditions, dual to a is three-dimensional analogue of Toda novel 3d W-algebra symmetry. By embedding in partial twist five-dimensional maximally supersymmetric Yang-Mills on manifold corners, we argue this two-dimensional topological sigma model A-branes moduli space...