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- Császár, Á. 52 (%)
- Noiri, T. 42 (%)
- Kátai, I. 36 (%)
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## On almost symmetric sequences inL p

### Acta Mathematica Hungarica (1989-09-01) 54: 269-278 , September 01, 1989

## An extension of Van Vleck’s functional equation for the sine

### Acta Mathematica Hungarica (2016-10-01) 150: 258-267 , October 01, 2016

In [7] H. Stetkær obtained the solutions of Van Vleck’s functional equation
$$ f (x\tau(y)z_0) - f(xyz_0) = 2f(x)f(y), \quad x, y \in S $$
for the sine where *S* is a semigroup,
$${\tau}$$
is an involution of *S* and *z*_{0} is a fixed element in the center of *S*. The purpose of this paper is to determine the complex-valued solutions of the following extension of Van Vleck’s functional equation for the sine
$$ \mu(y)f (x\tau(y)z_0) - f(xyz_0) = 2f(x)f(y),\quad x, y \in S$$
where
$${\mu : S\to \mathbb{C}}$$
is a multiplicative function such that
$${\mu (x\tau(x))=1}$$
for all
$${{x\in S}}$$
. Furthermore, we obtain the solutions of a variant of Van Vleck’s functional equation
$$ \mu(y)f (\sigma(y)xz_0) - f(xyz_0) = 2f(x)f(y), \quad x, y \in M $$
for the sine on a monoid *M*, where
$${\sigma}$$
is an involutive automorphism of *M*.

## On invariant ccc σ-ideals on $2^{\mathbb{N}}$

### Acta Mathematica Hungarica (2014-08-01) 143: 367-377 , August 01, 2014

We study structural properties of the collection of all *σ*-ideals in the *σ*-algebra of Borel subsets of the Cantor group
$2^{\mathbb{N}}$
, especially those which satisfy the countable chain condition (ccc) and are translation invariant. We prove that the latter collection contains an uncountable family of pairwise orthogonal members and, as a consequence, a strictly decreasing sequence of length *ω*_{1}.

We also make some observations related to the *σ*-ideal *I*_{ccc} on
$2^{\mathbb{N}}$
, consisting of all Borel sets which belong to every translation invariant ccc *σ*-ideal on
$2^{\mathbb{N}}$
. In particular, improving earlier results of Recław, Kraszewski and Komjáth, we show that:

every subset of
$2^{\mathbb{N}}$
of cardinality less than
can be covered by a set from *I*_{ccc},

there exists a set *C*∈*I*_{ccc} such that every countable subset *Y* of
$2^{\mathbb{N}}$
is contained in a translate of *C*.

## An extremum problem concerning algebraic polynomials

### Acta Mathematica Hungarica (1986-03-01) 47: 137-143 , March 01, 1986

## Individual stability and instability for evolutionary processes

### Acta Mathematica Hungarica (2017-09-07): 1-8 , September 07, 2017

We study the individual behaviour of uniform and nonuniform evolutionary processes. In [2] R. Datko gave a necessary and sufficient condition for the uniform exponential stability of an evolutionary process in Banach space. Our aim is to show that for a single vector *x* and not global, as Datko did in his paper, the trajectory of an evolutionary process on that vector *x* is exponentially stable.

## NON-CLASSICAL ASYMPTOTICS OF THE TRACE OF THE HEAT KERNEL FOR THE MAGNETIC SCHRÖDINGER OPERATOR

### Acta Mathematica Hungarica (2002-05-01) 94: 155-172 , May 01, 2002

We consider the effect of a magnetic field for the asymptotic behavior of the trace of the heat kernel for the Schrödinger operator. We discuss the case where the operator has compact resolvents in spite of the fact that the electric potential is degenerate on some submanifold. According to the degree of the degeneracy, we obtain non-classical asymptotics.

## Notes on lacunary interpolation with splines. III

### Acta Mathematica Hungarica (1987-03-01) 50: 33-37 , March 01, 1987

## On left self distributive rings

### Acta Mathematica Hungarica (1996-03-01) 71: 121-122 , March 01, 1996

## On the boundedness, Christensen measurability and continuity of t-Wright convex functions

### Acta Mathematica Hungarica (2013-10-01) 141: 68-77 , October 01, 2013

We discuss the connections between boundedness and continuity of *t*-Wright convex functions, moreover, we generalize some results of P. Fischer and Z. Słodkowski [4] concerning the Christensen measurability of Jensen convex functions to the case of *t*-Wright convex functions.

## On $$ \mathcal{C} $$ *-sets and decompositions of continuous and ηζ-continuous functions

### Acta Mathematica Hungarica (2007-12-01) 117: 325-333 , December 01, 2007

The main purpose of this paper is to introduce the concepts of
$$
\mathcal{C}
$$
*-sets,
$$
\mathcal{C}
$$
*-continuous functions and to obtain new decompositions of continuous and *η*ζ-continuous functions. Moreover, properties of
$$
\mathcal{C}
$$
*-sets and some properties of
$$
\mathcal{C}
$$
-sets are discussed.