Related papers: Eigenspaces of Coleman's Trace Operator

Koopman operator theory is shown to be directly related to the renormalization group. This observation allows us, with no assumption of translational invariance, to compute the critical exponents $\eta$ and $\delta$, as well as ratios of…

The main result of the paper is a description of the class of functions on the unit circle, for which Krein's trace formula holds for arbitrary pairs of unitary operators with trace class difference. We prove that this class of functions…

In this paper, we construct an infinite family of binary linear codes associated with double cosets with respect to certain maximal parabolic subgroup of the orthogonal group O(2n+1,q). Here q is a power of two. Then we obtain an infinite…

We consider perturbations of Minkowski space as well as more general spacetimes on which the wave operator $\square_g$ is known to be essentially self-adjoint. We define complex powers $(\square_g-i\varepsilon)^{-\alpha}$ by functional…

We deduce trace properties for modulation spaces of Gelfand-Shilov distributions. We use these properties to show that pseudo-differential operators with amplitudes in suitable modulation spaces, agree with pseudo-differential operators of…

Kobayashi recently proved that the generalized Heegner cycles of Bertolini--Darmon--Prasanna can be interpolated along the anticyclotomic tower, giving rise to distribution valued cohomology classes with expected growth rate. We interpolate…

Let $d\ge 1$ be an integer. We use the methods introduced by Lue Pan to prove that the compactly supported cohomology of Lubin-Tate towers and Drinfeld towers are isomorphic, as $\text{GL}_{d+1}(L)\times D_{L,\frac{1}{d+1}}^\times$-modules.

A variation of the Scott analysis of countable structures is applied to actions of non-Archimedean TSI Polish groups acting continuously on a Polish spaces. We give results on the potential Borel complexity spectrum of such groups, and…

We generalize von Neumann's well-known trace inequality, as well as related eigenvalue inequalities for hermitian matrices, to Schatten-class operators between complex Hilbert spaces of infinite dimension. To this end, we exploit some…

In this article a study was made of the conditions under which a Hamiltonian which is an element of the complex $ \left\{ h (1) \oplus h(1) \right\} \uplus u(2) $ Lie algebra admits ladder operators which are also elements of this algebra.…

Let $p$ be a prime number, $K$ a finite unramified extension of $\mathbb{Q}_p$ and $\mathbb{F}$ a finite extension of $\mathbb{F}_p$. For $\overline{\rho}$ any reducible two-dimensional representation of $\operatorname{Gal}(\overline{K}/K)$…

Using completions of certain universal enveloping algebras, we provide a natural setting for families of defining relations for the principal subspaces of standard modules for untwisted affine Lie algebras. We also use the theory of vertex…

Exterior power operations on the higher $K$-groups of a quasi-compact scheme have recently been constructed by Taelman and the authors by purely algebraic means. In this paper, we prove two formulae that help to compute these operations.…

Let M_m be the generic fibre of the formal deformation space of a one-dimensional formal module X of finite height together with level-m-structures. We show that it is defined over the mth Lubin-Tate extension of the ground field and that…

It is shown that the heat operator in the Hall coherent state transform for a compact Lie group $K$ is related with a Hermitian connection associated to a natural one-parameter family of complex structures on $T^*K$. The unitary parallel…

The classification of the local Galois representations using $(\varphi,\Gamma)$-modules by Fontaine has been generalized by Kisin and Ren over the Lubin-Tate extensions of local fields using the theory of $(\varphi_q,\Gamma_{LT})$-modules.…

The main aim of this paper is to generalize the classical concept of positive operator, and to develop a general extension theory, which overcomes not only the lack of a Hilbert space structure, but also the lack of a normable topology. The…

The paper establishes the Krein and Koplienko trace formulas for multivariable operator functions on symmetrically normed ideals of bounded operators. Results are proved for self-adjoint and maximal dissipative operators. They cover both…

Let $\Gamma$ be a countable abelian semigroup and $A$ be a countable abelian group satisfying a certain finiteness condition. Suppose that a group $G$ acts on a $(\Gamma \times A)$-graded Lie superalgebra ${\frak L}=\bigoplus_{(\alpha,a)…

Let F be a non-archimedean local field. The construction of Lubin-Tate $(\phi_q, \Gamma)$-modules attached to p-adic representations of $G_F$ depends on the choice of a uniformizer of F. In this paper, we give a description of a functor…