Conveners
Analysis and its Applications
- Ilko Brnetić (University of Zagreb, Faculty of Electrical Engineering and Computing)
Analysis and its Applications
- Dragana Jankov Maširević
Analysis and its Applications
- Dijana Ilišević (University of Zagreb)
Analysis and its Applications
- Julije Jakšetić (University of Zagreb)
Analysis and its Applications
- Lenka Mihoković (University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, Croatia)
In this talk we give general Opial type inequality. We
consider two functions, convex and concave and prove a new general inequality on a measure space $(\Omega,\Sigma,\mu)$. The obtained inequalities are not direct generalizations of the Opial inequality but are of Opial type because the integrals contain function and its integral representation. We apply our result to new Green functions...
The Hanin inequality is a kind of a reverse of the non-weighted arithmetic-quadratic mean inequality defined for non-negative real $n$-tuples, involving maxima of the corresponding $n$-tuple.
In this talk, our goal is to extend the Hanin inequality in several directions. We first give two-parametric extension of the basic inequality, as well as its refinement. Then, we discuss the...
The extension of the weighted Montgomery identity is established by using the general integral formula. Further, by using this extended weighted Montgomery identity for functions whose derivatives of order $n-1$ are absolutely continunous functions, new inequalities of the weighted Hermite-Hadamard type are obtained. Also, applications of these results are given for various types of weight function.
Extensions of Stolarsky's and Pinelis' inequalities are considered. New results of that type for q-integrals are obtained.
The first story concerns the real integral expression for the normalization constant $Z(\lambda, \nu)$ which occurs in the Conway-Maxwell distribution which is a generalization of the Poisson law. It turns out that $Z(\lambda, \nu)$ can be connected to the Le Roy-type hypergeometric function.
The second part of the talk resolves the representation of the Pólya constant in terms of...
Applications of modified Bessel functions frequently occur in statistics, for instance, it is a constituting term of the probability density function of the non-central $\chi^2$ distribution, having $n$ degrees of freedom and non-centrality parameter $\lambda>0$. The random variable with such distribution is usually denoted by $\chi_n'^{\;2}(\lambda)$.
Bearing in mind a great application...
Spaces invariant under unitary group representations have been extensively studied in the recent decades due to their importance in various areas, such as the theory of Gabor systems, wavelets and approximation theory. Dual integrable representations form a large and important class among the unitary representations, for which the properties of the cyclic subspaces and their generating orbits...
We present a fundamentally new proof of the dimensionless L^p boundedness of the Bakry Riesz vector on manifolds with bounded geometry. The key ingredients of the proof are sparse domination and probabilistic representation of the Riesz vector. This type of proof has the significant advantage that it allows for a much stronger conclusion, giving us a new range of weighted estimates. The talk...
On the one hand, the classical Banach-Stone theorem shows that the topological structure of a compact Hausdorff space $\Omega$ is determined by the geometry of $C(\Omega)$, the Banach space of continuous scalar-valued functions on $\Omega$, while on the other hand, it gives an explicit description of surjective linear isometries between two Banach spaces of continuous functions, $C(\Omega_1)$...
In this talk we establish new upper bounds for the norm of the sum of two Hilbert space operators and their Kronecker product. The obtained results extend some previously known results from the set of positive operators to arbitrary ones and refine several existing bounds. In particular, applications of the established bounds include refining celebrated numerical radius inequalities and the...
By using the interpolation of Jensen's inequality and the integral representation of multivariate B-splines, an estimate of various moments of multivariate B-splines in the class of convex functions has been made.
The two-point Abel-Gontscharoff interpolation problem is a special case of the Abel-Gontscharoff interpolation problem introduced by Whittaker, Gontscharoff and Davis. Over the years, many generalizations of Steffensen's inequality and related identities connected to these generalizations have been established.
For the purpose of this talk, we will use the identities related to...
The concept of strong F-convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong F-concavity. Using this concept refinements of the Young inequality are given as a model case. A general form of...
The Nuttall function has a wide range of application, mostly in the communication theory and related areas. We obtain new integral and series representation formulas for the Nuttall function via hypergeometric and related special functions and derive the closed form formula in terms of upper incomplete gamma function which simplifies some known results. We also present the computational...
For three homogeneous symmetric bivariate means $K$, $M$, $N$, let
$$
\mathcal{R}(K,M,N)(s,t)=K\bigl(M\bigl(s,N(s,t)\bigr),M\bigl(N(s,t),t\bigr) \bigr)
$$ be their resultant mean--map. Mean $M$ is said to be stable (or balanced), if $\mathcal{R}(M,M,M)=M$. Mean $M$ is called $(K,N)$-sub(super)-stabilizable, if $\mathcal{R}(K,M,N)\le(\ge)\, M$, and $M$ is between $K$ and $N$, where $K$ and...
