on utilizing the spectral representation of selfadjoint operators in hilbert spaces, some error bounds in approximating $n$-time differentiable functions of selfadjoint operators in hilbert spaces via a taylor's type expansion are given.

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...

For Maxwell operators in Lipschitz domains, we describe all m-dissipative boundary conditions and apply this result to generalized impedance Leontovich including the cases of singular, degenerate, randomized coefficients. To end construct Riesz bases trace spaces associated with curl-operator introduce a modified version triple adapted specifics equations, namely, mixed-order duality related sp...

For a compact connected Riemannian n-manifold $$(\Omega ,g)$$ with smooth boundary, we explicitly calculate the first two coefficients $$a_0$$ and $$a_1$$ of asymptotic expansion $$\sum _{k=1}^\infty \mathrm{{e}}^{-t \tau _k^{\mp }}= a_0t^{-n/2} {\mp } a_1 t^{-(n-1)/2} +O(t^{1-n/2})$$ as $$t\rightarrow 0^+$$ , where $$\tau ^-_k$$ (respectively, ^+_k$$ ) is k-th Navier–Lamé eigenvalue on $$\Omeg...

This article presents a unified approach to the abstract notions of partial convolution and involution in $L^p$-function spaces over semi-direct product of locally compact groups. Let $H$ and $K$ be locally compact groups and $tau:Hto Aut(K)$ be a continuous homomorphism.  Let $G_tau=Hltimes_tau K$ be the semi-direct product of $H$ and $K$ with respect to $tau$. We define left and right $tau$-c...

Abstract In this article, we provide necessary and sufficient conditions for the existence of non-norm-attaining operators in $\mathcal {L}(E, F)$ . By using a theorem due to Pfitzner on James boundaries, show that if there exists relatively compact set K (in weak operator topology) such $0$ is an element its closure but it not norm-closed convex hull, then can guarantee does attain norm. This ...

We introduce a dark photon considering U(1) gauge extension of the standard model in particle physics. Provided that extra symmetry is unbroken, massless and has no coupling to electromagnetic current. Higher-dimensional operators describe interactions with particles model. investigate charged leptons via dipole operators, mainly focusing on lepton family-violating processes. present an improve...