Analysis and Mathematical Physics最新文献

In this paper we derive new symmetry and new expression for 6j-symbols of the unitary principal series representations of the (SL(2,mathbb {C})) group. This allowed us to derive for them the analogue of the Regge symmetry.

Let X be a compact strictly pseudoconvex embeddable CR manifold and let A be the Toeplitz operator on X associated with a Reeb vector field ({mathcal {T}}in {mathscr {C}}^infty (X,TX)). Consider the operator (chi _k(A)) defined by the functional calculus of A, where (chi ) is a smooth function with compact support in the positive real line and (chi _k(lambda ):=chi (k^{-1}lambda )). It was established recently that (chi _k(A)(x,y)) admits a full asymptotic expansion in k when (k) becomes large. The second coefficient of the expansion plays an important role in the further studies of CR geometry. In this work, we calculate the second coefficient of the expansion.

Recent studies on linear positive operators have led to the investigation of approximation properties of Szász–Mirkyan operators related to the modified Bessel function of order 0. In this paper, we analyse the asymptotic behavior of these operators, convergence theorems, Voronovskaya and Grüss-Voronovskaya type results. A comparative assessment with classical Szász–Mirakyan operators is also presented. These results may have an impact on wide branches of knowledge, such as probability theory, statistics, physical chemistry, optics, and computer science, especially signal processing.

For a compact Riemannian manifold (M, g) with boundary (partial M), the Dirichlet-to-Neumann operator (Lambda _g:C^infty (partial M)longrightarrow C^infty (partial M)) is defined by (Lambda _gf=left. frac{partial u}{partial nu }right| _{partial M}), where (nu ) is the unit outer normal vector to the boundary and u is the solution to the Dirichlet problem (Delta _gu=0, u|_{partial M}=f). Let (g_partial ) be the Riemannian metric on (partial M) induced by g. The Calderón problem is posed as follows: To what extent is (M, g) determined by the data ((partial M,g_partial ,Lambda _g))? We prove the uniqueness theorem: A compact connected two-dimensional Riemannian manifold (M, g) with non-empty boundary is determined by the data ((partial M,g_partial ,Lambda _g)) uniquely up to conformal equivalence.

In this paper, we investigate the nonexistence of solutions of certain nonlinear elliptic equations, focusing on solutions that are stable or stable outside a compact set, potentially unbounded, and sign-changing. Our primary methods include integral estimates, Pohozaev-type identity and the monotonicity formula. Our classification approaches as a sharp result, specifically, in the subcritical case (i.e, (1< p < frac{n+4}{n-4})), we establish the existence of a mountain pass solution with a Morse index of 1 in the subspace of (H^2 cap H_0^1(Omega )) that exhibits cylindrical symmetry.

In this paper, we first introduced two time scales based on the interval [a, b] and ( mathbb {Z} ). Then, by using one of these time scale and substitutions rules, we prove a new version of discrete Hermite-Hadamard inequality for discrete convex functions. Moreover, we investigate the fractional version of this inequality involving fractional delta and nabla sums.

We prove the existence of unique global weak solutions to equations describing the sediment flow in the evolution of fluvial land surfaces, with constant water depth. These equations describe the so-called transport-limited situation, where all the sediment can be transported away given enough water. This is in distinction to the detachment-limited situation where we must wait for rock to weather (to sediment) before it can be transported away. Earlier work shows that these equations describe the optimal transport of sediment and the evolution of the surfaces in optimal transport theory. The existence theory is also extended to include diffusion in the water and the land surfaces.

In this paper we show that, given a planar Reifenberg flat domain with small constant and a divergence form operator associated to a real (not necessarily symmetric) uniformly elliptic matrix with Lipschitz coefficients, the Hausdorff dimension of its elliptic measure is at most 1. More precisely, we prove that there exists a subset of the boundary with full elliptic measure and with (sigma )-finite one-dimensional Hausdorff measure. For Reifenberg flat domains, this result extends a previous work of Thomas H. Wolff for the harmonic measure.

In this paper we prove the boundedness of the generalized fractional integral operator (I_{rho }) on generalized Morrey spaces with variable growth condition, which is an improvement of previous results, and then, we establish the boundedness of (I_{rho }) on their bi-preduals. We also prove the boundedness of (I_{rho }) on their preduals by the duality.

Bourgain–Morrey spaces, introduced by J. Bourgain, play an important role in the analysis of some linear and nonlinear partial differential equations. In this article, by exploiting the exquisite geometrical structure of shifted dyadic systems in the Euclidean space, we introduce (dyadic) Besov–Bourgain–Morrey–Campanato spaces via innovatively mixing together both the integral means from Campanato spaces and the structural framework of Besov–Bourgain–Morrey spaces (a recent generalization of Bourgain–Morrey spaces). We then study their fundamental real-variable properties, including the triviality and the nontriviality, their relations with other known function spaces, their predual spaces, as well as sharp John–Nirenberg type inequalities with distinct necessary and sufficient conditions which are different from the case of BMO and Campanato spaces. In particular, after establishing an equivalent quasi-norm of non-dyadic Besov–Bourgain–Morrey–Campanato spaces expressed via integrals, we characterize the boundedness of both Calderón–Zygmund operators and generalized fractional integrals on these non-dyadic function spaces and their predual spaces via vanishing conditions.