Related papers: Spectral Analysis Implies Spectral Synthesis

For convex and sequential effect algebras, we study spectrality in the sense of Foulis. We show that under additional conditions (strong archimedeanity, closedness in norm and a certain monotonicity property of the sequential product), such…

Positional encodings have enabled recent works to train a single adversarial network that can generate images of different scales. However, these approaches are either limited to a set of discrete scales or struggle to maintain good…

We give an upper bound on the number of the page on which the spectral sequence corresponding to a locally free isometric action of an abelian Lie group degenerates. We give examples showing that these bounds are indeed sharp. Finally, we…

We show that any abelian variety that is not affine has a nontrivial strongly abelian subvariety. In later papers in this sequence we apply this result to the study of minimal abelian varieties.

In this paper we make an attempt to extend L. Schwartz's classical result on spectral synthesis to several dimensions. Due to counterexamples of D. I. Gurevich this is impossible for translation invariant varieties. Our idea is to replace…

The geometric Langlands program is distinguished in assigning spectral decompositions to all representations, not only the irreducible ones. However, it is not even clear what is meant by a spectral decomposition when one works with…

In their previous work, the authors studied the abelian sandpile model on graphs constructed from a growing piece of a plane or space tiling, given periodic or open boundary conditions, and identified spectral factors which govern the…

This paper introduces the notion of local spectral expansion of a simplicial complex as a possible analogue of spectral expansion defined for graphs. We then show that the condition of local spectral expansion for a complex yields various…

In this paper, we study the spectrality of infinite convolutions in $\mathbb{R}^d$, where the spectrality means the corresponding square integrable function space admits a family of exponential functions as an orthonormal basis. Suppose…

In this paper, we study existence, equivalence and spectrality of infinite convolutions which may not be compactly supported in $d$-dimensional Euclidean space by manipulating various techniques in probability theory. First, we define the…

We study spectral properties of nonselfadjoint rank one perturbations of compact selfadjoint operators. The problems under consideration include completeness of eigenvectors, relations between completeness of the perturbed operator and its…

We present a contribution to the structure theory of locally compact groups. The emphasis is on compactly generated locally compact groups which admit no infinite discrete quotient. It is shown that such a group possesses a characteristic…

In this paper we study closed subspaces of ultradifferentiable functions which are invariant under the differentiation operator. We propose a version of spectral synthesis which takes into account the presence of non-trivial differentiation…

Let $A$ be an abelian variety over an algebraically closed field. We show that $A$ is the automorphism group scheme of some smooth projective variety if and only if $A$ has only finitely many automorphisms as an algebraic group. This…

If X is a compact Hausdorff space, supplied with a homeomorphism, then a crossed product involutive Banach algebra is naturally associated with these data. If X consists of one point, then this algebra is the group algebra of the integers.…

We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.

We extend the results by Froelich and Spronk and Turowska on the connection between operator synthesis and spectral synthesis for A(G) to second countable locally compact groups G. This gives us another proof that one-point subset of G is a…

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.

In this article we present an extensive survey on the developments in the theory of non-abelian finite groups with abelian automorphism groups, and pose some problems and further research directions.

In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$…