Related papers: Spectral calculations on locally convex vector spa…
Using the extrapolation of one-sided weights, we establish the boundedness of commutators generated by weighted Lipschitz functions and one-sided singular integral operators from weighted Lebesgue spaces to weighted one-sided…
We construct a Lipschitz function on $\er^{2}$ which is locally convex on the complement of some totally disconnected compact set but not convex. Existence of such function disproves a theorem that appeared in a paper by L. Pasqualini and…
We formulate a conjectural Lefschetz formula for locally symmetric spaces of finite volume. The formula can be verified in the compact case and for Riemann surfaces.
This work is concerned with the convex analysis of functions defined on (not necessarily finite-dimensional) Hilbert spaces whose values depend solely on a certain ``spectrum'' of the arguments, a class we term ``spectral functions.'' We…
The aim of this article is to explore in all remaining aspects the spectral theory of locally normal operators. In a previous article we proved the spectral theorem in terms of locally spectral measures. Here we prove the spectral theorem…
In the paper under review, we construct complex powers of multivalued linear operators with polynomially bounded $C$-resolvent existing on an appropriate region of the complex plane containing the interval $(-\infty,0].$ In our approach,…
In this note we provide a full conjugacy and subdifferential calculus for convex convex-composite functions in finite-dimensional space. Our approach, based on infimal convolution and cone-convexity, is straightforward and yields the…
In this work we investigate semigroups of operators acting on noncommutative $L^p$-spaces. We introduce noncommutative square functions and their connection to sectoriality, variants of Rademacher sectoriality, and $H^\infty$ functional…
We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave-convex term. We characterize completely the range of parameters for which solutions of the…
The paper proposes a vector generalization of the basic concepts of the theory of complex variable: the concept of modulus and argument of complex number. The author introduces some generalizations of the notion of holomorphic functions and…
The scalar functional determinants on sectors of the two-dimensional disc and spherical cap are determined for arbitrary angles (rational factors of $\pi$). The wholesphere and hemisphere expressions are also given, in low dimensions, for…
We show for a certain class of operators $A$ and holomorphic functions $f$ that the functional calculus $A\mapsto f(A)$ is holomorphic. Using this result we are able to prove that fractional Laplacians $(1+\Delta^g)^p$ depend real…
We study Fourier and Laplace transforms for Fourier hyperfunctions with values in a complex locally convex Hausdorff space. Since any hyperfunction with values in a wide class of locally convex Hausdorff spaces can be extended to a Fourier…
We study the action of some generalized integral operators of Bergman type on pointwise multipliers of holomorphic Triebel-Lizorkin spaces. We construct nontrivial examples of pointwise multipliers in Hardy-Sobolev spaces and give…
We construct a functor from the Hecke category to a groupoid built from the underlying Coxeter group. This fixes a gap in an earlier work of the authors. This functor provides an abstract realization of the localization of the Hecke…
We study Caratheodory-Herglotz functions whose values are continuous operators from a locally convex topological space which admits the factorization property into its conjugate dual space. We show how this case can be reduced to the case…
We give a sharp convexity estimate for L-functions which have a functional equation and an Euler product.
We study $H^1$ versus $C^1$ local minimizers for functionals defined on spaces of symmetric functions, namely functions that are invariant by the action of some subgroups of $\mathcal{O}(N)$. These functionals, in many cases, are associated…
We prove some existence results for a class of nonlinear fractional equations driven by a nonlocal operator.
We address a linearity problem for differentiable vectors in representations of infinite-dimensional Lie groups on locally convex spaces, which is similar to the linearity problem for the directional derivatives of functions.