Related papers: Algebraic aspects of spectral theory
Starting from a description of various generalized function algebras based on sequence spaces, we develop the general framework for considering linear problems with singular coefficients or non linear problems. Therefore, we prove…
The present text surveys some relevant situations and results where basic Module Theory interacts with computational aspects of operator algebras. We tried to keep a balance between constructive and algebraic aspects.
In this paper, we propose an abstract definition of dependent type theories as essentially algebraic theories. One of the main advantages of this definition is its composability: simple theories can be combined into more complex ones, and…
We provide sufficient conditions for systems of polynomial equations over general (real or complex) algebras to have a solution. This generalizes known results on quaternions, octonions and matrix algebras. We also generalize the…
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
On the one hand the algebras of linear operators here act on finite-dimensional vector spaces, and on the other hand the point of view is generally an analysts'. Also, one might think of algebras as being used to add more data to basic…
The article is designed to explain to commutative algebraists what spectra (in the sense of algebraic topology) are, why they were originally defined, and how they can be useful for commutative algebra.
After an historical introduction on the standard algebraic approach to quantum mechanics of large systems we review the basic mathematical aspects of the algebras of unbounded operators. After that we discuss in some details their relevance…
This note recapitulates and expands the contents of a tutorial on the mathematical theory of algebraic effects and handlers which I gave at the Dagstuhl seminar 18172 "Algebraic effect handlers go mainstream". It is targeted roughly at the…
We study the spectra of certain integro-differential equations arising in applications. Under some conditions on the kernel of the integral operator, we describe the non-real part of the spectrum.
The bispectral problem is motivated by an effort to understand and extend a remarkable phenomenon in Fourier analysis on the real line: the operator of time-and-band limiting is an integral operator admitting a second-order differential…
A summary of noncommutative spectral geometry as an approach to unification is presented. The role of the doubling of the algebra, the seeds of quantization and some cosmological implications are briefly discussed.
We study the scattering of particles and quasiparticles in the framework of algebraic quantum field theory. The main novelty is the construction of inclusive scattering matrix related to inclusive cross-sections. The inclusive scattering…
We characterize the spectrum (and its parts) of operators which can be represented as G=A+BC for a simpler operator A and a structured perturbation BC. The interest in this kind of perturbations is motivated, e.g., by perturbations of the…
We use spectral theory to produce embeddings of distributions in the algebras of generalized functions on a closed Riemannian manifold. These embeddings are invariant under isometries and preserve the singularity structure of the…
The tools, ideas, and insights from linear algebra, abstract algebra, and functional analysis can be extremely useful to signal processing and system theory in various areas of engineering, science, and social science including…
Linear algebra is usually defined over a field such as the reals or complex numbers. It is possible to extend this to skew fields such as the quaternions. However, to the authors' knowledge there is no commonly accepted notation of linear…
We prove some basic results on the dimension theory of algebraic stacks, and on the multiplicities of their irreducible components, for which we do not know a reference.
We present in this paper some fundamental tools for developing matrix analysis over the complex quaternion algebra. As applications, we consider generalized inverses, eigenvalues and eigenvectors, similarity, determinants of complex…
Representations of nonnegative polynomials as sums of squares are central to real algebraic geometry and the subject of active research. The sum-of-squares representations of a given polynomial are parametrized by the convex body of…