The Cesàro-Denjoy-Bochner scale of almost periodicity

, —— , . , f, ——, —. .     

A generalized Laplace transform of generalized functions

- . . . , .     

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.     

Extension of functions,which are traces of functions belonging to 249-01249-01249-01on an arbitrary subset of the line

( , k) , ER f(x) f(x)H _k (R) (k2— ,=(t) — k- ). f(x) E (t).     

On the distribution of points of maximal deviation in complex Čebyšev approximation

f — , . p _n (f) f . , n+2 , f–p _n (f) . , n . , .

---

On the distribution of points of maximal deviation in complex ebyev approximation

     

Spectral orders and convolution

. (R) _{– –} fg(y)h(x–y) dx dy _{– –} f ^{^} (x)g ^{^} (y)h ^{^} (x–y)dx dy (f,g0) —:f×gf ^{^} ×g ^{^}(f,g 0) f^{^} g^{^} f g -, X — . , - f ₁f ₂ , f ₁ ^{^} ×gf ₂×g 0g. .     

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.     

Limiting behavior of certain mixtures of distributions

U — [0, 1] Y — . X=[1–U ^1/v /Y], U Y.     

Investigation of Haar and Franklin series in Hardy spaces

(L ¹,H) (, ) , ; H — . , , L ¹ . [13] , . , , , .     

Converse results on equiconvergence of interpolating polynomials

, n- n- 1 , . , , ( « ») f .     

О простых идеалах первой степени

.      

On imbedding of certain function classes in symmetric spaces

2— - , () — - (), (, ) (0< <)— - . , >1; ; > ; ₁(), ₂() — -;f(x) — —. , () — ( , X, L , , ( ) -.

---

---

The author thanks Prof. M. K. Potapov for having proposed the problem and for the help he has given in the work.     

Role of information in the stochastic zero-sum differential game

In this paper, a linear-quadratic Gaussian zero-sum differential game is studied. Maneuverability is defined to measure players' strength. It is shown that a more maneuverable player would prefer a more observable information system. An example is given to show that a more controllable player might not prefer more observable measurements in the stochastic environment.The research reported in this paper was made possible through support extended to the Division of Engineering and Applied Physics, Harvard University, by the US Office of Naval Research under the Joint Services Electronics Program by Contract No. N00014-75-c-0648 and by the National Science Foundation under Grant No. GK31511.     

On the angular derivative and univalence

f . , , — , A f f(). , , f() 0 . , , ,A , f . , f() - f() . , , . (1976) ( ¦f(z)¦<1) . . (1969) ( ).     

On a test of Jordan type for double Fourier series with respect to multiplicative systems

. , , .     

Intrinsic definition of the Colombeau algebra of generalized functions

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

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.     

Pointwise convergence of expansions with respect to certain product systems

- , - _n A_n-,. , . , ¦_n¦=1 (n=1,2, ), . , — — , .     

Über den algorithmischen Nachweis von Ungleichungen I

We shall develop a method to prove inequalities in a unified manner. The idea is as follows: It is quite often possible to find a continuous functional : ⁿ , such that the left- and the right-hand side of a given inequality can be written in the form (u)(v) for suitable points,v=v(u). If one now constructs a map ^{n n} , which is functional increasing (i.e. for each x ⁿ (which is not a fixed point of ) the inequality (x)<((x)) should hold) one specially gets the chain (u)( u))( ²(u))... ⁿ (u)). Under quite general conditions one finds that the sequence { ⁿ (u)} _n converges tov=v(u). As a consequence one obtains the inequality (u)(v).     

Orthonormal systems satisfying an inequality of S. M. Nikol'skii

N- (p, q) (1 pN-, L _p - L _q -. , , , L L _q - , , .