Analysis and Mathematical Physics最新文献

This paper investigates the zero distribution of the expression ( F = f^n P(z,f) - a ), where ( f ) is a transcendental meromorphic function of hyper-order less than one, ( a not equiv 0 ) is a small function with respect to ( f ), and ( P(z,f) ) is a non-vanishing delay-differential polynomial with small coefficients. We introduce the notions of sum-degree and sum-weight of ( P(z,f) ), and use them to formulate conditions under which ( F ) has sufficiently many zeros. We also study paired delay-differential expressions of the form ( F_1 = f_1^{n_1} P_1(z, f_2) - a ) and ( F_2 = f_2^{n_2} P_2(z, f_1) - a ), and establish conditions on (P_1 (z,f_2)) and (P_2 (z,f_1)) to ensure that at least one of the functions ( F_1 ) or ( F_2 ) has infinitely many zeros.

Suppose a Lie group G acts on a vertex algebra (mathcal {V}). In this article we construct a vertex algebra ({tilde{V}}), which is an extension of (mathcal {V}) by a big central vertex subalgebra identified with the algebra of functionals on the space of regular (mathfrak {g})-connections ((textrm{d}+A)). The category of representations of ({tilde{mathcal {V}}}) fibres over the set of connections, and the fibres should be viewed as ((textrm{d}+A))-twisted modules of (mathcal {V}), generalizing the familiar notion of g-twisted modules. In fact, another application of our result is that it proposes an explicit definition of ((textrm{d}+A))-twisted modules of (mathcal {V}) in terms of a twisted commutator formula, and we feel that this subject should be pursued further. Vertex algebras with big centers appear in practice as critical level or large level limits of vertex algebras. In particular, we have in mind limits of the generalized quantum Langlands kernel, in which case G is the Langland dual and (mathcal {V}) is conjecturally the Feigin-Tipunin vertex algebra and the extension ({tilde{mathcal {V}}}) is conjecturally related to the Kac-DeConcini-Procesi quantum group with big center. With the current article, we can give a uniform and independent construction of these limits.

In the paper, we give necessary and sufficient conditions for a continuous on ([-pi ,pi ]) function f to belong various generalized Lipschitz classes defined by the Jacobi-Dunkl translation in terms of Fourier-Jacobi-Dunkl coefficients. As a corollary, we obtain analogues of Boas equivalence results and their extensions due to Tikhonov and Moricz. Also, we give sufficient conditions for generalized absolute convergence of Fourier-Jacobi-Dunkl series and show its sharpness in important (L^2) case using a new variant of inverse approximation theorem.

In this paper, we derive the sharp Bohr type inequalities for the Cesáro operator, Bernardi integral operator, discrete Fourier transform and discrete Laplace transform acting on the class of bounded analytic functions defined on shifted disks

In this paper, we revisit the boundedness and compactness of the commutator of the Cauchy–Szegő projection on a bounded strictly pseudoconvex domain (Omega ) with smooth boundary (partial Omega ), and establish the Schatten class estimate of such commutator via studying the structures of the local Besov space and establishing Taylor’s expansion on (partial Omega ).

In this article, we discuss the coefficients problems for Bloch functions. A general theorem on the sharp estimate of the weighted sum of the absolute values of squares of coefficients of Bloch functions is proved. Using this theorem, for fixed (0<rle 1/sqrt{3},) we improve a result of I.R. Kayumov and K.-J. Wirths (Monat. Math. 190, 123–135 (2019)), namely we improve the upper bound for the infimum of the set of numbers a(r) such that the value (S_rf-a(r)|f^{prime }(0)|^2,) where (S_rf) is the area functional, attains its maximum in the Bloch class at some monomial. The obtained estimate is asymptotically sharp as (rrightarrow 0.)

We extend the theory of exterior differential systems from manifolds and their tangent bundles to Lie algebroids. In particular, we define the concept of an integral manifold of such an exterior differential system. We support our developments with several examples, including an application to dynamical systems with a symmetry group and to the invariant inverse problem of the calculus of variations.

We study the inverse problem of reconstructing symmetric m-tensor fields in (mathbb {R}^n) from generalized Radon transforms, which arise naturally in areas such as medical imaging, seismology, and tomography. We introduce longitudinal and transversal Radon transforms, along with their momentum variants, which extend classical Radon transforms to tensor fields. We provide explicit kernel characterizations and establish invertibility modulo these kernels. Furthermore, we show that symmetric m-tensor fields can be uniquely recovered from suitable combinations of introduced transforms. Our results provide a mathematical foundation for imaging of tensor-valued physical quantities, going beyond scalar tomography.

In this paper, we present new fixed point theorems for sets that are endowed with a quasi-metric, which is a generalization of a metric space, where the triangle inequality is modified into a less restrictive form known as the relaxed triangle inequality: (mathfrak {D}_{q}(x,y) le s[mathfrak {D}_{q}(x,z) + mathfrak {D}_{q}(z,y)]), (s ge 1.) Furthermore, we apply our results to iterated function system theory to generate fractals, showcasing their usefulness in fractal construction. At the end, we discuss how sensitivity on maps carry over to their products and same for iterated function systems in the framework of quasi-metric spaces.

This paper investigates a p-Laplace higher-order hyperbolic equation with strong and weak damping terms and a superlinear source:

in (Omega times (0,T_{textrm{max}})), subject to null Navier boundary conditions. Here, (Omega subset {mathbb {R}}^n) is a bounded open domain. By using the Banach contraction mapping principle, we establish the well-posedness of weak solutions. When (q + 1 le p), we prove that all the weak solutions remain globally bounded. For (q + 1 > p), within the potential well framework, we derive the global existence of solutions for both critical and subcritical initial energy cases, accompanied by distinct decay estimates for global solutions when (q+1 > p), initial energy (E(0) le d) and Nehari functional (I(u_0)ge 0). Additionally, under specific exponent conditions (e.g., (2le m+1< p < q+1) for negative initial energy, (max {p, m+1}<q+1) for non-negative initial energy), we characterize finite-time blow-up of solutions under both positive and negative initial energy conditions. Using an auxiliary function method, we further demonstrate finite-time blow-up for linear weak damping with subcritical initial energy, and derive the bounds for the blow-up time.