摘要:

This paper is devoted to a self-contained approach to Mellin-type differential equations and associated ssampling expansions. Here the first order differential operator is not the normal d/dx but DM,c=xd/dx+c,c E R being connected with the definition of the Mellin transform. Existence and uniqueness theorems are established for a system of first order Mellin equations and the properties of nth order linear equations are investigated. Then self adjoint Mellin-type second order Sturm-Liouville eigenvalue problems are considered and properties of the eigenvalues, eigenfunctions and Green's functions are derived. As applications. sampling representations for two classes of integral transforms arising from the eigenvalue problem are introduced. In the first class the kernesl are solutions of the problem and in the second they are expressed in terms of green's function.

ISSN:0163-0563    

DOI:10.1080/01630560008816937

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

In this paper we consider the numerical stability of fast algorithms for discrete cosine transform (DCT) of type III and II, respectively. We show that various fast DCTs can possess a very different behaviour of numerical stability. By matrix factorizations we find that a complex fast DCT which is based mainly on a fast Fouier transform has a better numerical stability than a real fast DCT despite its larger arithmetical complexity. Numerical tests illustrate our theoretical results.

ISSN:0163-0563    

DOI:10.1080/01630560008816938

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

Computations with univariate polynomials, like the evaluation of product, quotient, remainder, greatest common divisor, etc, are closely related to linear algebra computations performed with structured matrices having the Toeplitz-like or the Hankel-like structures.

ISSN:0163-0563    

DOI:10.1080/01630560008816939

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

ABSTRACT. We shall apply the sampling method to compute the eigenvalues of a regular Sturm Liouville problem when a boundary condition contains the eigenvalue parameter. Truncation errors will be worked out and help us obtain eigenvalue enclosures. Examples are provided to illustrate the theory.

ISSN:0163-0563    

DOI:10.1080/01630560008816940

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

.

ISSN:0163-0563    

DOI:10.1080/01630560008816941

出版商:Marcel Dekker, Inc    

年代:2000

数据来源: Taylor

摘要:

Yeh defined a convolution of functionals on classical Wiener space and investigated the relationship between the Fourier-Wiener transforms of functionals in certain classes and the Fourier-Wiener transform of their convolution. Yoo extended Yeh's results to abstract Wiener space. In this paper, we introduce the intergal transform and convolution of analytic functionals on abstract Wiener space. And we establish the relationship between the integral transforms of exponential type of analytic functionals and the integral transform of theor convolution. Also we obtain Parseval's and Plancherel's relations for those functionals from this relationship. The main results of Yeh and Yoo then follow from our results as corollaries.

ISSN:0163-0563    

DOI:10.1080/01630560008816942

出版商:Marcel Dekker, Inc    

年代:2000

数据来源: Taylor

摘要:

In this paper, we study an approximation method for solving singular integral equations with conjugation on an open arc. The stability of the method depends on the invertibility of certain operators which belong to well-known algebras. We investigate properties of these operators and show how to choose the parameters of the approximation method so that the Fredholm indices of the operators mentioned become equal to zero.

ISSN:0163-0563    

DOI:10.1080/01630560008816943

出版商:Marcel Dekker, Inc    

年代:2000

数据来源: Taylor

摘要:

This survey is devoted to one of the most general Laplace-type integral transforms, the so-called Obrechkoff integral transform, introduced and studied for the first time by Obrechkoff[25]. It has been modified by Dimovski [5],[6] and used as a basis of a Mikusinski-type operational calculus for the hyper-Bessel differential operators of arbitrary order. Later, in a series of papers Dimovski and Kiryakova [8],[9],[10] have found operational properties, complex and real inversion formulas, Abel-type theorems for the Obrechkoff transform. This theory has been further developed by Kiryakova [16],[17],[18] using the tools of the Meijer's G-functions and of the fractional calculus. Namely, a new definition as a G-transform has been given for the Obrechkoff transform. The hyper-Bessel operators themselves, have given rise to a new generalized fractional calculus and further extensive use of the G-functions. Many other generalized differentiation and integration operators happen to be special cases in this calculus, too. Special cases of the Obrechkoff transform have been "rediscovered" later by many authors. We give examples how their results could be derived from the general ones surveyed here.

ISSN:0163-0563    

DOI:10.1080/01630560008816944

出版商:Marcel Dekker, Inc    

年代:2000

数据来源: Taylor

摘要:

Hardy (1919) proved that the space Lp(T), 1 ⩽ p ⩽ ∞, is invariant under (C, 1)-transformation of Fourier coefficients. This transformation may be considered as a linear integral operator H: Lp(T) → Lp(T), 1 ⩽ p ⩽ ∞. In this paper we show that the operator H is unbounded in the space BMO(T) of periodic functions of bounded mean oscillation. For the conjugate operator B introduced by Bellman (1944) B: Lq(T) → Lq(T), 1/ρp + 1/rho;q = 1, the boundedness of B in BMO(T) is proved directly without duality argument. An example is given to show that B is unbounded in H(T).

ISSN:0163-0563    

DOI:10.1080/01630560008816945

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor

摘要:

By means of an additional substitution a parabolic control problem with some nonlinear boundary condition will be decoupled into some control problem with linear parabolic state equations and an appropriate nonlinear mapping. This separation allows the use of efficient techniques e.g. Fourier methods, to determine the solution of linear parabolic state equations. Essential properties of the mapping used in the transformation are studied. Further, the application of piecewise constant discretizations of the controls in connection with the proposed splitting is discussed.

ISSN:0163-0563    

DOI:10.1080/01630560008816946

出版商:Marcel Dekker, Inc.    

年代:2000

数据来源: Taylor