Volume 51 , issue 3$-$4 ( 1999 ) | back |

Simultaneous approximation and Chebyshev centres in metric spaces | 61$-$68 |

**Keywords:** Best simultaneous approximation, Chebyshev centres.

**MSC:** 41A28, 41A50

General representation of pseudoinverses | 69$-$76 |

**Abstract**

In this paper we investigate general representations of various classes of generalized inverses for bounded operators over Hilbert and Banach spaces. These representations are expressed by means of the full-rank decomposition of bounded operators and adequately selected operators.

**Keywords:** Full-rank factorization,
reflexive generalized inverses, Moore-Penrose inverse, Drazin inverse.

**MSC:** 47A05, 15A09

A class of growth and bounds of solutions of a differential equation | 77$-$80 |

**Abstract**

We consider a class of nonlinear equations which admit characteristic equations. If the roots of this algebraic equation are real and distinct, the growth and bounds of solutions of the differential equation exist. An example is given which illustrates mentioned problems. An example of equation that is similar illustrates the problem of the existence of unique solutions.

**MSC:** 34C11

Convergence of a finite difference method for the third BVP for Poisson's equation | 81$-$89 |

**Abstract**

In this paper we study the convergence of finite difference schemes to weak solutions of the third boundary value problem for Poisson's equation on the unit square. Using the theory of interpolation of function spaces, we obtain error estimates in a discrete $W^1_2$ Sobolev norm consistent, or ``almost'' consistent, with the smoothness of the data.

**Keywords:** Third Boundary Value
Problems, Finite Difference Schemes, Sobolev Spaces, Interpolation of
Function Spaces, Convergence Rate Estimates.

**MSC:** 65N15, 46B70

Relationship between the operators of Cauchy and logarithmic potential type | 91$-$96 |

**Abstract**

Asymptotic behaviour of singular values, together with the estimate of the remainder term, of Cauchy operator and the operator of logarithmic potential type, as well as the corresponding trace formula are determined.

**Keywords:** Cauchy integral operator, operator
of logarithmic potential type, singular values, trace formula.

**MSC:** 47B10, 47G10, 45C05

On uniform convergence of spectral expansions and their derivatives arising by self-adjoint extensions of an one-dimensional Schrödinger operator | 97$-$110 |

**Abstract**

In this paper we consider the problem of global uniform convergence of spectral expansions and their derivatives, $\sum_{n=1}^{\infty}f_nu^{(j)}_n(x)$ $(j=0,1,\dots)$, generated by non-negative self-adjoint extensions of the operator $\Cal L(u)(x) = - u^{\prime\prime}(x) + q(x)u(x)$ with discrete spectrum, for functions from the class $W^{(1)}_2(G)$, where $G$ is a finite interval of the real axis. Two theorems giving conditions on functions $q(x)$, $f(x)$ which are sufficient for the absolute and uniform convergence on $\overline G$ of the mentioned series, are proved. Also, some convergence rate estimates are obtained.

**Keywords:** Spectral expansion, global uniform convergence, Schrödinger
operator.

**MSC:** 34L10

50 years since the first congress and foundation assembly of the Union of the Societies of Mathematicians and Physicists of Yugoslavia | 111$-$116 |

**Abstract**

The paper contains a brief exposition of the 50 years of history of the Union of Mathematicians, Physicists (and Astronomers) of Yugoslavia, which was founded on November 12th, 1949 at Bled.

**MSC:** 01A74

Sedamdesetogodišnjica rodjenja Dušana Adnadjevića | 117$-$119 |