This article is concerned with a spectral optimization problem: in smooth bounded domain $${\Omega }$$ , for function m and nonnegative parameter $$\alpha $$ consider the first eigenvalue $$\lambda _\alpha (m)$$ of operator $${\mathcal {L}}_m$$ given by {L}}_m(u)= -{\text {div}} \left( 1+\alpha m)\nabla u\right) -mu$$ . Assuming uniform pointwise integral bounds on m, we investigate issue minim...

6 The multiplier space and other spaces intrinsic to D theory 24 6.1 Multipliers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 6.2 The weakly factored space D D and its dual . . . . . . . . . . . 25 6.3 The Corona Theorem . . . . . . . . . . . . . . . . . . . . . . . . 27 6.3.1 The ∂-equation in the Dirichlet Space . . . . . . . . . . . 28 6.3.2 Corona Theorems and Complete Nev...

The class of species sampling mixture models is introduced as an extension of semiparametric models based on the Dirichlet process to models based on the general class of species sampling priors, or equivalently the class of all exchangeable urn distributions. Using Fubini calculus in conjunction with Pitman (1995, 1996), we derive characterizations of the posterior distribution in terms of a p...

We study composition operators of characteristic zero on weighted Hilbert spaces Dirichlet series. For this purpose, we demonstrate the existence mean counting functions associated with series symbol, and provide a corresponding change variables formula for operator. This leads to natural necessary conditions boundedness compactness. Bergman-type spaces, are able show that compactness condition...

This paper is concerned with the variational approach in weighted Sobolev spaces to timeharmonic elastic scattering by two-dimensional unbounded rough surfaces. The rough surface is supposed to be the graph of a bounded and uniformly Lipschitz continuous function, on which the total elastic displacement satisfies either the Dirichlet or impedance boundary condition. We establish uniqueness and ...

We attach a certain n × n matrix An to the Dirichlet series L(s) = ∑ ∞ k=1 akk . We study the determinant, characteristic polynomial, eigenvalues, and eigenvectors of these matrices. The determinant of An can be understood as a weighted sum of the first n coefficients of the Dirichlet series L(s). We give an interpretation of the partial sum of a Dirichlet series as a product of eigenvalues. In...