• 대한수학회논문집
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• 제32권4호
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• pp.875-883
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• 2017

In this work, we establish Heisenberg-type uncertainty principle for the Bessel-Struve Fock space ${\mathbb{F}}_{\nu}$ associated to the Airy operator $L_{\nu}$. Next, we give an application of the theory of extremal function and reproducing kernel of Hilbert space, to establish the extremal function associated to a bounded linear operator $T:{\mathbb{F}}_{\nu}{\rightarrow}H$, where H be a Hilbert space. Furthermore, we come up with some results regarding the extremal functions, when T are difference operators.

• 대한수학회보
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• 제59권6호
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• pp.1371-1385
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• 2022

For setting a general weight function on n dimensional complex space ℂⁿ, we expand the classical Fock space. We define Fock type space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ of entire functions with a mixed norm, where 0 < p, q < ∞ and t ∈ ℝ and prove that the mixed norm of an entire function is equivalent to the mixed norm of its radial derivative on $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$. As a result of this application, the space $F^{p,q}_{{\phi},t}({\mathbb{C}}^n)$ is especially characterized by a Lipschitz type condition.

• 대한수학회보
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• 제56권3호
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• pp.745-756
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• 2019

We obtain Lipschitz type characterization and double integral characterization for Fock-type spaces with the norm $${\parallel}f{\parallel}^p_{F^p_{m,{\alpha},t}}\;=\;{\displaystyle\smashmargin{2}{\int\nolimits_{{\mathbb{C}}^n}}\;{\left|{f(z){e^{-{\alpha}}{\mid}z{\mid}^m}}\right|^p}\;{\frac{dV(z)}{(1+{\mid}z{\mid})^t}}$$, where ${\alpha}>0$, $t{\in}{\mathbb{R}}$, and $m{\in}\mathbb{N}$. The results of this paper are the extensions of the classical weighted Fock space $F^p_{2,{\alpha},t}$.

• East Asian mathematical journal
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• 제33권1호
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• pp.37-44
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• 2017

We will prove size estimates of the Bergman kernel for the generalized Fock space ${\mathcal{F}}^2_{\varphi}$, where ${\varphi}$ belongs to the class $\mathcal{W} $. The main tool for the proof is to use the estimate on the canonical solution to the ${\bar{\partial}}$-equation. We use Delin's weighted $L^2$-estimate ([3], [6]) for it.

• 대한수학회보
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• 제60권4호
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• pp.957-969
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• 2023

Let j be a nonnegative integer. We define the Toeplitz-type operators T^(j)_a with symbol a ∈ L^∞(C), which are variants of the traditional Toeplitz operators obtained for j = 0. In this paper, we study the boundedness of these operators and characterize their compactness in terms of its Berezin transform.

• 대한수학회지
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• 제54권6호
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• pp.1801-1816
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• 2017

We study some spectral properties of Volterra-type integral operators $V_g$ and $I_g$ with holomorphic symbol g on the Fock-Sobolev spaces ${\mathcal{F}}^p_{{\psi}m}$. We showed that $V_g$ is bounded on ${\mathcal{F}}^p_{{\psi}m}$ if and only if g is a complex polynomial of degree not exceeding two, while compactness of $V_g$ is described by degree of g being not bigger than one. We also identified all those positive numbers p for which the operator $V_g$ belongs to the Schatten $S_p$ classes. Finally, we characterize the spectrum of $V_g$ in terms of a closed disk of radius twice the coefficient of the highest degree term in a polynomial expansion of g.

• East Asian mathematical journal
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• 제35권1호
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• pp.1-7
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• 2019

We consider the initial value problem of the Schrodinger equation for an interesting Cauchy-Euler type operator ${\mathfrak{R}}$ on ${\mathbb{C}}^n$ that is an analogue of the harmonic oscillator in ${\mathbb{R}}^n$. We get an appropriate $L^1-L^{\infty}$ dispersive estimate for the solution of the initial value problem.