Related papers: Arithmetic differential operators on Z_p

Let X be a set of analytic functions on the open unit disk D, and let phi be an analytic function on D such that phi(D) is contained in D and f |-> f o phi takes X into itself. We present conditions on X ensuring that if f |-> f o phi is…

A periodic linear graph operator acts on states (functions) defined on the vertices of a graph equipped with a free translation action. Fourier transform with respect to the translation group reveals the central spectral objects, Bloch and…

Sufficient conditions are given for a function $F(p)$, analytic in Re$p>0$, to be a Laplace transform of a function $f(t)$, such that $max_{t\ge 0}|f(t)|<\infty$, $f(0)=0$.

Applying Baxter's method of the Q-operator to the set of Sekiguchi's commuting partial differential operators we show that Jack polynomials P(x_1,...,x_n) are eigenfunctions of a one-parameter family of integral operators Q_z. The operators…

Let function $f$ be analytic in the unit disk ${\mathbb D}$ and be normalized so that $f(z)=z+a_2z^2+a_3z^3+\cdots$. In this paper we give sharp bounds of the modulus of its second, third and fourth coefficient, if $f$ satisfies \[…

Let $K$ be any unital commutative $\mathbb Q$-algebra and $z=(z_1, ..., z_n)$ commutative or noncommutative free variables. Let $t$ be a formal parameter which commutes with $z$ and elements of $K$. We denote uniformly by $\kzz$ and…

Firstly we establish a sharp pointwise estimate for the arbitrary derivative of the function $f\in F_{\alpha}^{p},$ where $F_{\alpha}^{p}$ denotes the Fock space for $1\leq p<\infty.$ Then, in a particular Hilbert case when $p=2$ we…

For the self-adjoint operator of the $p$th derivative, a system of fundamental solutions is constructed. This system is analogues to the classical system of sines and cosines. The properties of such functions are studied. Classes of…

A dynamically affine map is a finite quotient of an affine morphism of an algebraic group. We determine the rationality or transcendence of the Artin-Mazur zeta function of a dynamically affine self-map of $\mathbb{P}^1(k)$ for $k$ an…

We consider a smooth hyper-surface Z of a closed Riemannian manifold X. Let P be the Poisson operator associating to a smooth function on Z its harmonic extension on X\Z. If A is a pseudo-differential operator on X of degree <3, we prove…

We characterize Hilbert spaces in the class of all Banach spaces using Fourier transform of vector-valued functions over the field $Q_p$ of $p$-adic numbers. Precisely, Banach space $X$ is isomorphic to a Hilbert one if and only if Fourier…

In this paper, we define the subclasses $R_{\mu,p}^{\delta}(\alpha;A,B)\ $ and $ P_{\mu,p}^{\delta}(\alpha;A,B)\ $ of analytic functions in the open unit disc of complex plain. Then the neighborhood properties, integral means inequalities…

The definition for the $p$-adic Hurwitz-type Euler zeta functions has been given by using the fermionic $p$-adic integral on $\mathbb Z_p$. By computing the values of this kind of $p$-adic zeta function at negative integers, we show that it…

The purpose of this paper is to study a class of ill-posed differential equations. In some settings, these differential equations exhibit uniqueness but not existence, while in others they exhibit existence but not uniqueness. An example of…

It is an open problem whether a separating operator acting between semiprime f-algebras is a weighted composition operator ( <cite>AAB</cite>). We prove that the answer is positive if and only if the separating operator is almost…

H. J. Schwartz proved in his thesis (1969) that a nonzero bounded operator on Hardy spaces $(H^p, 1\leq p\leq\infty)$ is almost multiplicative if and only if it is a composition operator. But, his proof has a gap. In this article, we show…

We prove that $p$-determinants of a certain class of differential operators can be lifted to power series over $\mathbb{Q}$. We compute these power series in terms of monodromy of the corresponding differential operators.

We establish, for $1 < p < \infty$, higher order $\mathcal{S}^p$-differentiability results of the function $\varphi : t\in \mathbb{R} \mapsto f(A+tK) - f(A)$ for selfadjoint operators $A$ and $K$ on a separable Hilbert space $\mathcal{H}$…

In this paper, we establish a condition on the coefficients of differential operators generated in the space of square-integrable functions on the entire real line by an ordinary differential expression with periodic, complex-valued…

We show that the p-operator in the Witt algebra (the restricted Lie algebra of derivations of the quotient of the polynomial algebra over a field of characteristic p by the ideal generated by the p-th power of the indeterminant) is given by…