In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

Let $\Gamma(\mathcal{H})$ be the boson Fock space over a finite dimensional Hilbert $\mathcal{H}$. It is shown that every gaussian symmetry admits Klauder-Bargmann integral representation in terms of coherent states. Furthermore, symmetries, states and second quantization contractions, all these operators belong to weakly closed, selfadjoint semigroup $\mathcal{E}_2(\mathcal{H})$ bounded $\Gamm...

We consider a generic modified logarithmic Sobolev inequality (mLSI) of the form $\mathrm{Ent}_{\mu}(e^f) \le \tfrac{\rho}{2} \mathbb{E}_\mu e^f \Gamma(f)^2$ for some difference operator $\Gamma$, and show how it implies two-level concentration inequalities akin to Hanson--Wright or Bernstein inequality. This can be applied continuous (e.\,g. sphere bounded perturbations product measures) as we...

The global existence and stability of the solution to delay differential equation (*)$\dot{u} = A(t)u + G(t,u(t-\tau)) f(t)$, $t\ge 0$, $u(t) v(t)$, $-\tau \le t\le are studied. Here $A(t):\mathcal{H}\to \mathcal{H}$ is a closed, densely defined, linear operator in Hilbert space $\mathcal{H}$ $G(t,u)$ nonlinear continuous with respect $u$ $t$. We assume that spectrum $A(t)$ lies half-plane $\Re...

We study the modular symmetric standard-model effective field theory. employ stringy Ansatz on coupling structure that 4-point couplings $y^{(4)}$ of matter fields are written by a product 3-point $y^{(3)}$ fields, i.e., $y^{(4)} = y^{(3)}y^{(3)}$. In this framework, we discuss flavor bilinear fermion operators and 4-fermion operators, where holomorphic anti-holomorphic forms appear. From Ansat...

Abstract We show that stationary characters on irreducible lattices $\Gamma < G$ Γ < G of higher-rank connected semisimple Lie groups are conjugation invariant, is, they genuine characters. This result has several applications in representation theory, operator algebras...

We study several families of vertex operator superalgebras from a jet (super)scheme point view. provide new examples algebras which are “chiral-quantizations" their $$C_{2}$$ -algebras $$R_V$$ . Our come affine $$C_\ell ^{(1)}$$ -series algebras, $$\ell \geqslant 1$$ , certain $$N=1$$ superconformal Feigin–Stoyanovsky principal subspaces, type graph $$W_{\Gamma }$$ and extended Virasoro algebra...

We formulate the Riemannian calculus of probability set embedded with $$L^2$$ -Wasserstein metric. This is an initial work transport information geometry. Our investigation starts simplex (probability manifold) supported on vertices a finite graph. The main idea to embed manifold as submanifold positive measure space weighted graph Laplacian operator. By this viewpoint, we establish torsion–fre...

we consider the transitive linear maps on the operator algebra $b(x)$for a separable banach space $x$. we show if a bounded linear map is norm transitive on $b(x)$,then it must be hypercyclic with strong operator topology. also we provide a sot-transitivelinear map without being hypercyclic in the strong operator topology.

Using exclusively the localized estimates upon which helicoidal method was built by authors, we show how sparse can also be obtained. This approach yields a domination for scalar and multiple vector-valued extensions of operators alike. We illustrate these ideas an $n$-linear Fourier multiplier whose symbol is singular along $k$-dimensional subspace $\Gamma={\xi\_1+\cdots+\xi\_{n+1}=0}$, where ...