On an application of infinitely divisible distributions to quadrature problems

— - , .     

О Распределении Значений Целой Функции Ро Аргументам

.      

Fortsetzungssätze und Moduln über Semifields

. . — . — —.

---

---

Herrn Professor Dr. Frank Terpe zum 60. Geburtstag gewidmet     

Central limit theorems for Walsh series with general gaps

. [1]. 3 - .     

Moduli of smoothness and best approximation in the spacesL p , 0<p<1

L ^p , 0<<1, .     

Sharp Nikolskii inequalities with exponential weights

w _a(x)=exp(–x^a), xR, a0. , N _n (a,p,q) — (2), _n P _nw_ap, CN_n(a,p, q)P_nw_aq. , — , {P _n}, .

---

---

This material is based upon research supported by the National Science Foundation under Grant No. DMS-84-19525, by the United States Information Agency under Senior Research Fulbright Grant No. 85-41612, and by the Hungarian Ministry of Education (first author). The work was started while the second author visited The Ohio State University between 1983 and 1985, and it was completed during the first author's visit to Hungary in 1985.     

О простых идеалах первой степени

.      

The Cesàro-Denjoy-Bochner scale of almost periodicity

, —— , . , f, ——, —. .     

Intrinsic definition of the Colombeau algebra of generalized functions

— G (), . . . , : , , D()G(), , , G(), , , , — .     

On certain imbedding and extension theorems for a weighted class of functions

n- , S n–1 m (0m<n), () S . () , ().     

On summability of subsequences of partial sums of trigonometric Fourier series

n- (n1) fL ^p ([–, ] ⁿ ),=1 = (L C) . , , f([–, ] ⁿ ).     

On the solution of a generalized Schrödinger-type equation

Lu(t)+(u,F)g(t)=f(t), tS. , ( F, g). .

---

---

The authors wish to thank Professor Yu. A. Rozanov for his help and discussions.     

Additive functions

1<q<2 L:= _n=1 1/q ⁿ=1/q–1. [0,1] _n()=1, A _n:= _i=1 ^n–1 _i(x)/q^i+1/n x _n(x)=0, _n>. , = _{n=1 n}(x)/qⁿ. F: [0,L]R , F(x)= _{n=1 n}(x)a_n, _n=1 ¦a _n¦<. [0,L]. q(1,2), . , q(1, 2), . .     

Some inequalities of Hardy-Littlewood type

[3] , >0 n ^– a _n , . , . . , .

---

---

This research was partially supported by the Hungarian National Foundation for Scientific Research under Grant #234.     

Sharpening of Stečkin's theorem to strong approximation with exponentp

— , B _n , B p1., , p=1 , - . , , , p.     

On the bestL p multipoint local approximation

P (f) — , f L ^p - , k . f 02k–2 P (f) 0.     

Radon—Nikodym theorems for multimeasures and transition multimeasures

— . , — . , .

---

---

Research supported by N. S. F. Grant DMS-8802688.     

On cubature formulas on the basis of lattices

Q (.. , L). Q . P(S_r(2)) — 2 (S _r(2) (r — ). , M(P(S _r(m=sup{t(·)t(·)₁:t P(S _r(2)),t 0}. , /4+(1)M(P(S _r(2)))/r ²15/17+(1)(r+). (Q), Q L.     

On the asymptotic distribution of oscillation points in rational approximation

. . ( ) , , (m) (m)m, n(m) ^* ) ( d(m) — r _{m, n(m)} ^*) )/ , .

---

---

The paper was written during the second author's visit at the Mathematical Institute of the Hungarian Academy of Sciences.     

On strong summability of polynomial expansions

—.

---

---

Dedicated to Professor L. Leindler on his 50^th birthday