Projection minima of a symmetric convex body

R ⁿ n- , : RⁿPRⁿ/ o - . —

Some remarks on Turán's inequality. III: The completion

. 0pq, 1–1/p+1/p0. f(x) — n, [–1,1],

Sharpening of Stečkin's theorem to strong approximation

. . , , : f — ,

Blocks of orthogonal random variables and the strong law of large numbers

(X _k ),k=1,2,... — _k ² >1; (X _k ) , E(X _k X _t )=0 p k<>(p+1) (p,k,l=1, 2, ...) , , ,

On the Pólya conjecture concerning the maximum and minimum of the modulus of an entire function of finite order given by a lacunary power series

, (fz) , ,

Derivatives of the maximum modulus of a starlike function

. - , n=1,2, ...

Large-time behavior of perturbed diffusion markov processes with applications to the second eigenvalue problem for fokker-planck operators and simulated annealing

We study the large-time behavior and rate of convergence to the invariant measures of the processes dX (t)=b(X) (t)) dt + (X (t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/² , the transition density has a good lower bound and when the process has run for about exp( – )/², it is very close to the invariant measure. LetL =(²/2) – U · be a second-order differential operator on ^d. Under suitable conditions,L ^z has the discrete spectrum

New covering numbers and spectral properties of operators in Banach spaces

, , , . ., . — s- , . , s- (,s- ) ; _n (T), ¦ _l (T)¦¦ ₂ (T)¦...0, T:EE .

A class of strongly nonlinear functional differential equations

Let H be a real Hilbert space, :H [0, + ] a proper l.s.c., convex function with L_k:={u H; u² + (u) k} compact for every k > 0, let > 0 be a given constant and . We prove an existence result for strong solutions to a class of functional differential equations of the form

Comparative cooperative game theory

Given two side-payment gamesv andw, both defined for the same finite player-setN, the following three welfare criteria are characterized in terms of the datav andw: (A) For everyy C(w) there existsx C(v) such thatyx; (A) For everyxC(v) there existsyC(w) such thatyx; and (B) There existyC(w) andxC(v) such thatyx. (HereC(v) denotes the core ofv.) Given two non-side-payment gamesv andw, sufficient conditions for the criteria (A) and (B) are established, by observing that an ordinal convex game has a large core.In memory of my teacher in Japan, Professor Ryuichi Watanabe, 1928–1986.     

A test of convergence of Fourier series with respect to multiplicative systems,analogous to the Jordan test

, {p _n} _n=0 (p₀=1, _n2 n2). : x f(t) V(G)

On the preservation of periodic monotonicity

A 2-periodic continuous real functionf is said to beperiodically monotone if it has the following property: there exist numbert ₁t ₂t ₃t ₁+2 such thatf is nonincreasing fort ₁t ₂ and nondecreasing int ₂tt ₃. For any 2-periodic, integrable real functiong with ₀ ² |g(t|dt) we define

Spectral synthesis for Euler type operators

A=(a _ij) _i ^j=1 — k-o ,a _ij . :

Asymptotics of polynomials orthogonal with respect to varying measures

Letd be a finite positive Borel measure on the interval [0, 2] such that >0 almost everywhere; andW _n be a sequence of polynomials, degW _n =n, whose zeros (w _n ,1,,w _n,n lie in [|z|1]. Let d _n <> for each_nN, whered _n =d/|W _n (e ⁱ )|². We consider the table of polynomials _n,m such that for each fixednN the system _n,m,mN, is orthonormal with respect tod _n . If

A generalized Laplace transform of generalized functions

- . . . , .