Related papers: Total power operations in spectral sequences
The $E_2$ term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for a number of other spectral sequences. Our goal is to show how the higher terms of such spectral sequences are determined…
A general analytical approach to the statistical description of quantum graph spectra based on the exact periodic orbit expansions of quantum levels is discussed. The exact and approximate expressions obtained in \cite{Anima} for the…
The spectral action on the equivariant real spectral triple over \A(SU_q(2)) is computed explicitly. Properties of the differential calculus arising from the Dirac operator are studied and the results are compared to the commutative case of…
The one-loop effective action for a generic set of quantum fields is calculared as a nonlocal expansion in powers of the curvatures (field strengths). This expansion is obtained to third order in the curvature. It is stressed that the…
We investigate the pseudospectrum of the Kerr black hole, which indicates the instability of the spectrum of quasinormal modes (QNMs) of the Kerr black hole. Methodologically, we use the hyperboloidal framework to cast the QNM problem into…
In the mid 1980s, while working on establishing completion theorems for equivariant Algebraic K-Theory similar to the well-known completion theorems for equivariant topological K-theory, the late Robert Thomason found the strong finiteness…
The topology of spaces of Hermitian operators in $C^n$ with non-simple spectra was studied by V.Arnold in a relation with the theory of adiabatic connections and the quantum Hall effect. The natural filtration of these spaces by the sets of…
We show that a polynomial H(N) of degree N of a harmonic oscillator hamiltonian allows us to devise a fully solvable continuous quantum system for which the first N discrete energy eigenvalues can be chosen at will. In general such a choice…
In $G$-equivariant stable homotopy theory, it is known that the equivariant Eilenberg-Mac Lane spectra representing ordinary equivariant cohomology have nontrivial $RO(G)$-graded homotopy corresponding to the equivariant (co)homology of…
A C-motivic modular forms spectrum mmf has recently been constructed. This article presents detailed computational information on the Adams spectral sequence for mmf. This information is essential for computing with the C-motivic and…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
We reconsider the inference of spatial power spectra from angular clustering data and show how to include correlations in both the angular correlation function and the spatial power spectrum. Inclusion of the full covariance matrices…
We delineate the scope of research on the completeness of eigenstates in quantum mechanics. Based on the limit of the potential function at infinity, the proof of completeness is divided into eight cases, and theoretical proofs or numerical…
We consider elliptic second order partial differential operators with Lipschitz continuous leading order coefficients on finite cubes and the whole Euclidean space. We prove quantitative sampling and equidistribution theorems for…
This note compares two models of the equivariant homotopy type of the smash powers of a spectrum, namely the "Bokstedt smash product" and the Hill-Hopkins-Ravenel norm.
We determine the $RO(C_2)$-graded Hurewicz images of the $C_2$-equivariant Eilenberg--MacLane spectra $H\underline{\mathbb F_2}$, $H\underline{\mathbb Z}$ and $H\underline{A}$, where $\underline{\mathbb F_2}$ and $\underline{\mathbb Z}$…
This paper is concerned with the convergence of power sequences and stability of Hilbert space operators, where "convergence" and "stability" refer to weak, strong and norm topologies. It is proved that an operator has a convergent power…
We start by identifying a class of pseudo-differential operators, generated by the set of continuous negative definite functions, that are in the weak similarity (WS) orbit of the self-adjoint log-Bessel operator on the Euclidean space.…
We present a streamlined approach for generalized strong and norm convergence of self-adjoint operators in different Hilbert spaces. In particular, we establish convergence of associated (semi-)groups, (essential) spectra and spectral…
Angular anisotropy techniques for cosmic diffuse radiation maps are powerful probes, even for quite small data sets. A popular observable is the angular power spectrum; we present a detailed study applicable to any unbinned source skymap…