Related papers: Potpourri, 5
The statements in the title are explained and proved, as a little exercise in elementary normed vector space theory at the level of Chapter 5 of Dieudonn\'e's "Foundations of Mathematical Analysis". A connection to recent moment bounds for…
In these notes we briefly consider various situations related to infinite commutative semigroups, connected to convolutions and Fourier transforms.
These notes deal with some basic notions related to p-adic numbers and functions of p-adic numbers.
These informal notes consider Fourier transforms on a simple class of nice functions and some basic properties of the Fourier transform.
These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, using quaternions and Clifford algebras in higher dimensions. The main themes are weak solutions, the mean-value property, and subharmonicity.
The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.
This paper concerns the number of lattice points in a circle.
We study the convergence of the Laurent polynomials of Lagrange interpolation on the unit circle for continuous functions satisfying a condition about their modulus of continuity. The novelty of the result is that now the nodal systems are…
We give some remarks on some manifolds K3 surfaces, Complex projective spaces, real projective space and Torus and the classification of two dimensional Riemannian surfaces, Green functions and the Stokes formula. We also, talk about traces…
These informal notes briefly discuss some basic topics in harmonic analysis along the lines of convolutions and Fourier transforms.
These notes are devoted to the theory of exponential sums over finite fields. The first chapter recalls some of the number-theoretic interest of such sums. The second chapter discusses the $L$-functions attached to such sums, the "Weil…
Basic facts and definitions of conformal moduli of rings and quadrilaterals are recalled. Some computational methods are reviewed. For the case of quadrilaterals with polygonal sides, some recent results are given. Some numerical…
These notes are concerned with Abel sums and connections with analytic extensions of Fourier integrals.
In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.
In this paper, we compute the spectral norms of the matrices related with integer squences and we give some example related with Fibonacci, Lucas, Pell and Perrin numbers.
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
Chapter 1 deals with the problem of the existence of an upper/lower envelope from a convex cone or, more generally, a convex set for functions on the projective limit of vector lattices with values in the completion of the Kantorovich space…
We study the topology of polynomial functions by deforming them generically. We explain how the non-conservation of the total ``quantity'' of singularity in the neighbourhood of infinity is related to the variation of topology in certain…
This note is about variations on a theorem of Bers about short pants decompositions of surfaces. It contains a version for surfaces with boundary but also a slight improvement on the best known bound for closed surfaces.
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…