해석 함수의 Bessel 직교성

학위논문(석사) - 한국과학기술원 : 응용수학과, 1990.2, [ [ii], 17, [2] p. ; ]Bessel polynomials satisfy a specific condition, called Bessel orthogonality. The weight with respect to which Bessel polynomials are orthogonal is a hyperfunction with a point mass. We solve the problem (raised by E. Grosswald) of finding other set of functions that have this property.한국과학기술원 : 응용수학과

Sobolev 형의 직교성에 관하여

학위논문(박사) - 한국과학기술원 : 수학과, 1995.8, [ [ii], 65 p. ]We generalize the Skrzipek``s methods in the case of Sobolev type inner products and consider the following problem : Generate a sequence $\{Q_n\}$ of polynomials, $deg(Q_n)=n$, orthogonal with respect to inner product defined by $$(f,g)=\int_I fg\, d\mu+ \sum_{p,q=1}^K\sum_{i=0}^{n_p-1}\sum_{j=0}^{n_q-1} \lambda_{p,q}^{i,j} f^{(i)}(c_p)g^{(j)}(c_q),$$ where $d\mu$ is a positive measure on an interval I, $n_p$, $1\le p\le K$ are nonnegative intergers, $c_p\in R$ and $\lambda_{p,q}^{i,j}= \lambda_{q,p}^{j,i}\ge0$. Next, We are concerned with the representation formula and behavior of zeros of Sobolev orthogonal polynomials which are orthogonal relative to a Sobolev pseudo-inner product of type $$\phi (p,q) := \int_I p(x)q(x)\, d\sigma (x) + \int_{I^{\prime}} p^{\prime}(x) q^{\prime}(x)\, d\mu (x),$$ where $d\sigma$ and $d\mu\, (\ne 0)$ are Borel measures on intervals I and $I^{\prime}$ respectively.한국과학기술원 : 수학과