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Paley's and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions based on a complete orthonormal system of Dunkl kernels generalizing the classical exponential system defining the classical Fourier series.

Although the difficulties related to the Dunkl settings, the techniques used by K. Sato were still efficient in this case to establish the inequalities which have expected similarities with the classical case, and Hardy and Paley theorems for the Fourier–Bessel expansions due to the fact that the Bessel transform is the even part of the Dunkl transform.

Paley's inequality and Hardy's inequality are proved on a Hardy-type space for the Fourier–Dunkl expansions.

This work is a participation in extending the harmonic analysis associated with the Dunkl operators and it shows the utility of BMO spaces to establish some analytical results.

Dunkl theory is a generalization of Fourier analysis and special function theory related to root systems. Establishing Paley and Hardy's inequalities in these settings is a participation in extending the Dunkl harmonic analysis as it has many applications in mathematical physics and in the framework of vector valued extensions of multipliers.

In this paper, the authors take the first step in the study of constructive methods by using Sobolev polynomials.

To do that, the authors use the connection formulas between Sobolev polynomials and classical Laguerre polynomials, as well as the well-known Fourier coefficients for these latter.

Then, the authors compute explicit formulas for the Fourier coefficients of some families of Laguerre–Sobolev type orthogonal polynomials over a finite interval. The authors also describe an oscillatory region in each case as a reasonable choice for approximation purposes.

In order to take the first step in the study of constructive methods by using Sobolev polynomials, this paper deals with Fourier coefficients for certain families of polynomials orthogonal with respect to the Sobolev type inner product. As far as the authors know, this particular problem has not been addressed in the existing literature.

This investigation aims to determine the effect of trade uncertainty on domestic investment (DI) and foreign direct investment (FDI) for the Turkish economy from the first quarter of 2005 to the first quarter of 2020.

The authors adopt the vector autoregression (VAR) model augmented with Fourier terms. Using this methodology, the authors obtain the empirical results of the impulse-response functions and the variance decomposition analysis.

The empirical results demonstrate that a shock to trade uncertainty has a slight negative impact on DI for up to approximately 1.5 years, whereas its impact on FDI is negative but long-lasting. Moreover, the contribution of trade uncertainty to FDI is relatively higher than to DI in the error variance decomposition for the investigated period. These empirical results can be beneficial for shaping the Turkish authorities' trade policies in the following periods.

These findings have implications within the macroeconomic setting. Government authorities can provide tax exemptions for specified sectors and debureaucratize investment processes for both domestic and foreign entrepreneurs. Additionally, institutional quality and property rights should be protected strictly and developed gradually.

This study is the first to examine the impact of world trade uncertainty on Türkiye’s DI and FDI. Because trade uncertainty might act as fixed costs, this creates the option value of waiting and seeing the market, and firms hesitate to incur investment.

The purpose of this study aims to analyze the dynamic behavior of the relationship between atmospheric carbon emissions and the Organisation for Economic Co-operation and Development (OECD) industrial production index (IPI) in the short and long term by applying multifractal techniques.

Multifractal de-trended cross-correlation technique is used for this analysis based on the relevant literature. In addition, it is the most widely used approach to estimate multifractality because it generates robust empirical results against non-stationarities in the time series.

It is revealed that industrial production causes long and short term environmental costs. The OECD IPI and atmospheric carbon emissions were found to have a strong correlation between the time domain. However, this relationship does not mostly take into account the frequency-based correlations with the tail effects caused by shocks that are effective on the economy. In this study, the long-term dependence of the relationship between the OECD IPI and atmospheric carbon emissions differs from the correlation obtained by linear methods, as the analysis is based on the frequency. The major finding is that the Hurst coefficient is in the range 0.40-0.75 indicating.

In this study, the local singular behavior of the time-series is analyzed to test for the multifractality characteristics of the series. In this context, the scaling exponents and the singularity spectrum are obtained to determine the origins of this multifractality. The multifractal time series are defined as the set of points with a given singularity exponent a where this exponent a is illustrated as a fractal with fractal dimension f(α). Therefore, the multifractality term indicates the existence of fluctuations, which are non-uniform and more importantly, their relative frequencies are also scale-dependent.

The results provide information based on the fluctuation in IPI, which determines the main conjuncture of the economy. An optimal strategy for shaping the consequences of climate change resulting from industrial production activities will not only need to be quite comprehensive and global in scale but also policies will need to be applicable to the national and local conditions of the given nation and adaptable to the needs of the country.

The results provide information for the analysis of the environmental cost of climate change depending on the magnitude of the impact on the total supply. In addition to environmental problems, climate change leads to economic problems, and hence, policy instruments are introduced to fight against the adverse effects of it.

This study may be of practical and technical importance in regional climate change forecasting, extreme carbon emission regulations and industrial production resource management in the world economy. Hence, the major contribution of this study is to introduce an approach to sustainability for the analysis of the environmental cost of growth in the supply side economy.

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.

This paper aims to test purchasing power parity (PPP) hypothesis for Greece, Italy, Ireland, Portugal and Spain, which are known as the GIIPS countries.

The authors conduct a comprehensive analysis by using unit root approaches without and with structural breaks and non-linearity.

The PPP is valid for the GIIPS countries. Considering structural breaks in non-linear framework plays a crucial role.

There is no empirical study testing PPP hypothesis by focusing on the GIIPS countries. This study further takes into account for structural breaks and non-linearity in the real exchange rates of these countries.

This paper conducts an empirical analysis for the estimations of volume-weighted price of the Korean stock market and provides the implications of the estimation errors regarding the characteristics of the market and the corresponding securities. We employ fast Fourier transformation strategy and traditional simple average strategy and compare the performances of the two methods using five minute interval intra-day data of KOSPI50 stocks. Estimations errors of the two methods from Ex Post real VWAP are computed and the relationships between the errors and other market variables are examined. We find that larger market value leads to smaller error whereas average trading in dollar has negative relationship with the estimation error. We also look at the behavior of institutional traders and the order execution mechanism to explain our statistical findings.

This study aims to examine the hysteresis hypothesis in unemployment using monthly data from 13 countries in transition.

Stationarity in the unemployment rate of selected transition economies was analyzed using four different group unit root tests, namely, linear, structural breaks, non-linear and structural breaks and non-linear.

The empirical results show that the unemployment hysteresis hypothesis is valid for the majority of transition economies, including Bulgaria, Croatia, the Czech Republic, Estonia, Hungary, the Kyrgyz Republic, Latvia, Lithuania, Poland, Romania and Slovenia. However, the results strongly reject the null hypothesis of unemployment hysteresis for the Kazakhstan and the Slovak Republics.

This study revealed that, for countries in transition, advanced unit root tests exhibit greater validity when compared to standard tests

We study an efficient numerical method for pricing European options when the dynamics of the underlying asset are described by Levy processes. In this case. we can write a characteristic function solution for a specific Levy option model and then take its inversion numerically. Specifically we use Variance Gamma process as an example of Levy option model and consider various characteristic function representation forms of European option price such as Carr and Madan (1999), Bakshi and Madan (2000). and Lewis (2001). Fast Fourier Transform method is applied to solve the numerical inversion problem with parameters for the KOSPI 200 options data. After analysing the problems in the FFT method, we propose alternative numerical inversion method, Gaussian Quadrature. This paper reports that Gaussian Quadrature numerical inversion method with the representation form of Bakshi & Madan (2000) is more efficient and accurate than other alternatives considered in this paper.

Using a generalized translation operator, this study aims to obtain a generalization of Titchmarsh's theorem for the Laguerre–Bessel transform for functions satisfying the ψ-Laguerre–Bessel–Lipschitz condition in the space L²_α (K), where K=0,+∞×0,+∞[.

The author has employed the results developed by Titchmarsh, of reference number [1].

In this paper, an analogous of Titchmarsh's theorem is established for Laguerre–Bessel transform.

To the best of the authors’ findings, at the time of submission of this paper, the results reported are new and interesting.