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- Császár, Á. 52 (%)
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## Super-measures and finitely defined topological measures

### Acta Mathematica Hungarica (2003-04-01) 99: 33-42 , April 01, 2003

We introduce a class of set-functions on the set of natural numbers, which are called super-measures. Super-measures are then utilized to characterize a certain class of topological measures (previously called quasi-measures, see below) which arises naturally. The members of this class of topological measures are called finitely defined, and are shown to be dense in the set of all topological measures.

## On the control of a circular membrane. I

### Acta Mathematica Hungarica (1993-09-01) 61: 303-325 , September 01, 1993

## Almost sure linearity for signed rank statistics in the non-I.I.D. case

### Acta Mathematica Hungarica (1986-09-01) 48: 273-284 , September 01, 1986

## 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*.

## On compactly dominated spaces

### Acta Mathematica Hungarica (1986-09-01) 47: 313-319 , September 01, 1986

## 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.

## 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.