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For analytic operator functions, we prove accumulation of branches of complex eigenvalues to the essential spectrum. Moreover, we show minimality and completeness of the corresponding system of eigenvectors and associated vectors. These results are used to prove sufficient conditions for eigenvalue accumulation to the poles and to infinity of rational operator functions. Finally, an application of electromagnetic field theory is given. [ABSTRACT FROM AUTHOR]

In this paper, we prove a C 2 , α -estimate for the solution to the complex Monge–Ampère equation det ⁡ ( u i j ¯ ) = f with 0 < f ∈ C α , under the assumption that u ∈ C 1 , β for some β < 1 which depends on n and α . [ABSTRACT FROM AUTHOR]

We study a new notion of trace operators and trace spaces for abstract Hilbert complexes. We introduce trace spaces as quotient spaces/annihilators. We characterize the kernels and images of the related trace operators and discuss duality relationships between trace spaces. We elaborate that many properties of the classical boundary traces associated with the Euclidean de Rham complex on bounded Lipschitz domains are rooted in the general structure of Hilbert complexes. We arrive at abstract trace Hilbert complexes that can be formulated using quotient spaces/annihilators. We show that, if a Hilbert complex admits stable "regular decompositions" with compact lifting operators, then the associated trace Hilbert complex is Fredholm. Incarnations of abstract concepts and results in the concrete case of the de Rham complex in three-dimensional Euclidean space will be discussed throughout. [ABSTRACT FROM AUTHOR]

The aim of this paper is two fold. We show that if a complex function F on C operates in the modulation spaces M p , 1 ( R n ) by composition, then F is real analytic on R 2 ≈ C . This answers negatively, the open question posed in Ruzhansky et al. (2012) [21] , regarding the general power type nonlinearity of the form | u | α u . We also characterise the functions that operate in the modulation space M 1 , 1 ( R n ) . The local well-posedness of the NLS, NLW and NLKG equations for the ‘real entire’ nonlinearities are also studied in some weighted modulation spaces M s p , q ( R n ) . [ABSTRACT FROM AUTHOR]

Abstract: We study complex, classical, scalar fields within a new framework introduced in a previous work. We replace the usual functional integral by a complex functional arising from a boosted Hamiltonian. We generalize the Feynman–Kac relation to this setting, and use it to establish the spectral condition on a cylinder. We consider also positive-temperature states. [Copyright &y& Elsevier]

Abstract: For the truncated moment problem associated to a complex sequence to have a representing measure μ, it is necessary for the moment matrix to be positive semidefinite, and for the algebraic variety to satisfy as well as a consistency condition: the Riesz functional vanishes on every polynomial of degree at most 2n that vanishes on . In previous work with L. Fialkow and H.M. Möller, the first named author proved that for the extremal case ( ), positivity and consistency are sufficient for the existence of a representing measure. In this paper we solve the truncated moment problem for cubic column relations in of the form ( ); we do this by checking consistency. For in the open cone determined by , we first prove that the algebraic variety has exactly 7 points and ; we then apply the above mentioned result to obtain a concrete, computable, necessary and sufficient condition for the existence of a representing measure. [Copyright &y& Elsevier]

Abstract: For the cotangent bundle of a compact Lie group K, we study the complex-time evolution of the vertical tangent bundle and the associated geometric quantization Hilbert space under an infinite-dimensional family of Hamiltonian flows. For each such flow, we construct a generalized coherent state transform (CST), which is a unitary isomorphism between and a certain weighted -space of holomorphic functions. For a particular set of choices, we show that this isomorphism is naturally decomposed as a product of a Heisenberg-type evolution (for complex time −τ) within , followed by a polarization-changing geometric-quantization evolution (for complex time +τ). In this case, our construction yields the usual generalized Segal–Bargmann transform of Hall. We show that the infinite-dimensional family of Hamiltonian flows can also be understood in terms of Thiemannʼs “complexifier” method (which generalizes the construction of adapted complex structures). [Copyright &y& Elsevier]

Abstract: We give equivalent forms of the Askey–Wilson polynomials expressing them with the help of the Al-Salam–Chihara polynomials. After restricting parameters of the Askey–Wilson polynomials to complex conjugate pairs we expand the Askey–Wilson weight function in the series similar to the Poisson–Mehler expansion formula and give its probabilistic interpretation. In particular this result can be used to calculate explicit forms of ‘q-Hermite’ moments of the Askey–Wilson density, hence enabling calculation of all moments of the Askey–Wilson density. On the way (by setting certain parameter q to 0) we get some formulae useful in the rapidly developing so-called ‘free probability’. [Copyright &y& Elsevier]

Abstract: Property A is a non-equivariant analogue of amenability defined for metric spaces. Euclidean spaces and trees are examples of spaces with Property A. Simultaneously generalising these facts, we show that finite-dimensional cube complexes have Property A. We do not assume that the complex is locally finite. We also prove that given a discrete group acting properly on a finite-dimensional cube complex the stabilisers of vertices at infinity are amenable. [Copyright &y& Elsevier]

Abstract: We compare the above-mentioned article with the content of a previous publication. [Copyright &y& Elsevier]