In the last decade, considerable attention has been paid by graph theorists to the study of spectra of graphs and their interaction with structure and characteristic properties of graphs. After the 'classical' book by N. L. Biggs [12] on algebraic graph theory in general, the first comprehensive monograph on this particular topic, by D. M. Cvetkovic, M. Doob and H. Sachs [34], appeared in 1979....

Abstract We prove that if G is a discrete group and $$(A,G,\alpha )$$ ( A , G α ) C*-dynamical system such the reduced crossed product $$A\rtimes _{r,\alpha } G$$ ⋊ r...

Kardiologie und Angiologie II, Universitäts-Herzzentrum Freiburg-Bad Krozingen, Bad Krozingen; Universitäres Herz-und Gefäßzentrum Hamburg, Hamburg; Klinik und Poliklinik für Angiologie, Departement Herz und Gefässe, Universität Bern, Bern; Uniklinikum Heidelberg, Medizinische Klinik, Innere Medizin III, Heidelberg; Ev.-Luth. Diakonissenkrankenhaus, Abteilung Radiologie, Flensburg; Universitäts...

Kardiologie und Angiologie II, Universitäts-Herzzentrum Freiburg-Bad Krozingen, Bad Krozingen; Universitäres Herz-und Gefäßzentrum Hamburg, Hamburg; Klinik und Poliklinik für Angiologie, Departement Herz und Gefässe, Universität Bern, Bern; Uniklinikum Heidelberg, Medizinische Klinik, Innere Medizin III, Heidelberg; Ev.-Luth. Diakonissenkrankenhaus, Abteilung Radiologie, Flensburg; Universitäts...

The origin of Herz spaces is the study of characterization of functions and multipliers on the classical Hardy spaces ([1, 8]). By virtue of many authors’ works Herz spaces have became one of the remarkable classes of function spaces in harmonic analysis now. One of the important problems on the spaces is boundedness of sublinear operators satisfying proper conditions. Hernández, Li, Lu and Yan...

In this note, I review some basic properties of the Hopfield model. I closely follow Chapter 2 of Herz, Krogh & Palmer (1991) which is an excellent introductory textbook on the theory of neural networks. I motivate the mean field analysis of the stochastic Hopfield model slightly differently than Herz, Krogh & Palmer (1991) and my derivations are a little longer, filling in some of the gaps in ...

Bessel functions of matrix argument appeared as a subject of studies in the work of Herz [6]. One can find in the multivariate statistics literature some applications of these functions (see [11]). The main tool of Herz’s work was the Laplace transform and its inverse in the space of real symmetric matrices. He obtained several properties but a “good” differential system was lacking. This was t...

The boundedness for the multilinear Marcinkiewicz operators on certain Hardy and Herz-Hardy spaces are obtained.

The main goal of this article is to provide estimates mild solutions Navier–Stokes equations with arbitrary external forces in Rn for n≥2 on proposed weak Herz-type Besov–Morrey spaces. These spaces are larger than known and Herz considered works equations. Morrey–Sobolev based weak-Herz space denoted as WK˙p,qαMμs WK˙p,qαN˙μ,rs, respectively, represent new properties interpolations. This class...

For $p,q\in [1,\infty)$, we study the isomorphism problem for $p$- and $q$-convolution algebras associated to locally compact groups. While it is well known that not every group can be recovered from its von Neumann algebra, show this case $\mathrm{CV}_p(G)$ of $p$-convolvers $\mathrm{PM}_p(G)$ $p$-pseudomeasures, $p\neq 2$. More generally, if isometrically isomorphic $\mathrm{CV}_q(H)$, with $...