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Displaying similar documents to “Lower bounds for Schrödinger operators in H¹(ℝ)”

Best constants for the isoperimetric inequality in quantitative form

Marco Cicalese, Gian Paolo Leonardi (2013)

Journal of the European Mathematical Society

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We prove some results in the context of isoperimetric inequalities with quantitative terms. In the 2 -dimensional case, our main contribution is a method for determining the optimal coefficients c 1 , ... , c m in the inequality δ P ( E ) k = 1 m c k α ( E ) k + o ( α ( E ) m ) , valid for each Borel set E with positive and finite area, with δ P ( E ) and α ( E ) being, respectively, the 𝑖𝑠𝑜𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑟𝑖𝑐𝑑𝑒𝑓𝑖𝑐𝑖𝑡 and the 𝐹𝑟𝑎𝑒𝑛𝑘𝑒𝑙𝑎𝑠𝑦𝑚𝑚𝑒𝑡𝑟𝑦 of E . In n dimensions, besides proving existence and regularity properties of minimizers for a wide class of 𝑞𝑢𝑎𝑛𝑡𝑖𝑡𝑎𝑡𝑖𝑣𝑒𝑖𝑠𝑜𝑝𝑒𝑟𝑖𝑚𝑒𝑡𝑟𝑖𝑐𝑞𝑢𝑜𝑡𝑖𝑒𝑛𝑡𝑠 including the lower semicontinuous extension of δ P ( E ) α ( E ) 2 , we...

On the distribution of ( k , r ) -integers in Piatetski-Shapiro sequences

Teerapat Srichan (2021)

Czechoslovak Mathematical Journal

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A natural number n is said to be a ( k , r ) -integer if n = a k b , where k > r > 1 and b is not divisible by the r th power of any prime. We study the distribution of such ( k , r ) -integers in the Piatetski-Shapiro sequence { n c } with c > 1 . As a corollary, we also obtain similar results for semi- r -free integers.

Admissible spaces for a first order differential equation with delayed argument

Nina A. Chernyavskaya, Lela S. Dorel, Leonid A. Shuster (2019)

Czechoslovak Mathematical Journal

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We consider the equation - y ' ( x ) + q ( x ) y ( x - ϕ ( x ) ) = f ( x ) , x , where ϕ and q ( q 1 ) are positive continuous functions for all x and f C ( ) . By a solution of the equation we mean any function y , continuously differentiable everywhere in , which satisfies the equation for all x . We show that under certain additional conditions on the functions ϕ and q , the above equation has a unique solution y , satisfying the inequality y ' C ( ) + q y C ( ) c f C ( ) , where the constant c ( 0 , ) does not depend on the choice of f .

The boundedness of two classes of integral operators

Xin Wang, Ming-Sheng Liu (2021)

Czechoslovak Mathematical Journal

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The aim of this paper is to characterize the L p - L q boundedness of two classes of integral operators from L p ( 𝒰 , d V α ) to L q ( 𝒰 , d V β ) in terms of the parameters a , b , c , p , q and α , β , where 𝒰 is the Siegel upper half-space. The results in the presented paper generalize a corresponding result given in C. Liu, Y. Liu, P. Hu, L. Zhou (2019).

Capacitary estimates of positive solutions of semilinear elliptic equations with absorbtion

Moshe Marcus, Laurent Véron (2004)

Journal of the European Mathematical Society

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Let Ω be a bounded domain of class C 2 in N and let K be a compact subset of Ω . Assume that q ( N + 1 ) / ( N 1 ) and denote by U K the maximal solution of Δ u + u q = 0 in Ω which vanishes on Ω K . We obtain sharp upper and lower estimates for U K in terms of the Bessel capacity C 2 / q , q ' and prove that U K is σ -moderate. In addition we describe the precise asymptotic behavior of U K at points σ K , which depends on the “density” of K at σ , measured in terms of the capacity C 2 / q , q ' .

Differences of two semiconvex functions on the real line

Václav Kryštof, Luděk Zajíček (2016)

Commentationes Mathematicae Universitatis Carolinae

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It is proved that real functions on which can be represented as the difference of two semiconvex functions with a general modulus (or of two lower C 1 -functions, or of two strongly paraconvex functions) coincide with semismooth functions on (i.e. those locally Lipschitz functions on for which f + ' ( x ) = lim t x + f + ' ( t ) and f - ' ( x ) = lim t x - f - ' ( t ) for each x ). Further, for each modulus ω , we characterize the class D S C ω of functions on which can be written as f = g - h , where g and h are semiconvex with modulus C ω (for some C > 0 ) using a new...

A new characterization of symmetric group by NSE

Azam Babai, Zeinab Akhlaghi (2017)

Czechoslovak Mathematical Journal

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Let G be a group and ω ( G ) be the set of element orders of G . Let k ω ( G ) and m k ( G ) be the number of elements of order k in G . Let nse ( G ) = { m k ( G ) : k ω ( G ) } . Assume r is a prime number and let G be a group such that nse ( G ) = nse ( S r ) , where S r is the symmetric group of degree r . In this paper we prove that G S r , if r divides the order of G and r 2 does not divide it. To get the conclusion we make use of some well-known results on the prime graphs of finite simple groups and their components.

On upper bounds for total k -domination number via the probabilistic method

Saylí Sigarreta, Saylé Sigarreta, Hugo Cruz-Suárez (2023)

Kybernetika

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For a fixed positive integer k and G = ( V , E ) a connected graph of order n , whose minimum vertex degree is at least k , a set S V is a total k -dominating set, also known as a k -tuple total dominating set, if every vertex v V has at least k neighbors in S . The minimum size of a total k -dominating set for G is called the total k -domination number of G , denoted by γ k t ( G ) . The total k -domination problem is to determine a minimum total k -dominating set of G . Since the exact problem is in general quite difficult...

On a system of equations with primes

Paolo Leonetti, Salvatore Tringali (2014)

Journal de Théorie des Nombres de Bordeaux

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Given an integer n 3 , let u 1 , ... , u n be pairwise coprime integers 2 , 𝒟 a family of nonempty proper subsets of { 1 , ... , n } with “enough” elements, and ε a function 𝒟 { ± 1 } . Does there exist at least one prime q such that q divides i I u i - ε ( I ) for some I 𝒟 , but it does not divide u 1 u n ? We answer this question in the positive when the u i are prime powers and ε and 𝒟 are subjected to certain restrictions. We use the result to prove that, if ε 0 { ± 1 } and A is a set of three or more primes that contains all prime divisors of any...

Linear maps preserving A -unitary operators

Abdellatif Chahbi, Samir Kabbaj, Ahmed Charifi (2016)

Mathematica Bohemica

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Let be a complex Hilbert space, A a positive operator with closed range in ( ) and A ( ) the sub-algebra of ( ) of all A -self-adjoint operators. Assume φ : A ( ) onto itself is a linear continuous map. This paper shows that if φ preserves A -unitary operators such that φ ( I ) = P then ψ defined by ψ ( T ) = P φ ( P T ) is a homomorphism or an anti-homomorphism and ψ ( T ) = ψ ( T ) for all T A ( ) , where P = A + A and A + is the Moore-Penrose inverse of A . A similar result is also true if φ preserves A -quasi-unitary operators in both directions such that there...

On the unit group of a semisimple group algebra 𝔽 q S L ( 2 , 5 )

Rajendra K. Sharma, Gaurav Mittal (2022)

Mathematica Bohemica

Similarity:

We give the characterization of the unit group of 𝔽 q S L ( 2 , 5 ) , where 𝔽 q is a finite field with q = p k elements for prime p > 5 , and S L ( 2 , 5 ) denotes the special linear group of 2 × 2 matrices having determinant 1 over the cyclic group 5 .

Repdigits in generalized Pell sequences

Jhon J. Bravo, Jose L. Herrera (2020)

Archivum Mathematicum

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For an integer k 2 , let ( n ) n be the k - generalized Pell sequence which starts with 0 , ... , 0 , 1 ( k terms) and each term afterwards is given by the linear recurrence n = 2 n - 1 + n - 2 + + n - k . In this paper, we find all k -generalized Pell numbers with only one distinct digit (the so-called repdigits). Some interesting estimations involving generalized Pell numbers, that we believe are of independent interest, are also deduced. This paper continues a previous work that searched for repdigits in the usual Pell sequence ( P n ( 2 ) ) n . ...

A localization property for B p q s and F p q s spaces

Hans Triebel (1994)

Studia Mathematica

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Let f j = k a k f ( 2 j + 1 x - 2 k ) , where the sum is taken over the lattice of all points k in n having integer-valued components, j∈ℕ and a k . Let A p q s be either B p q s or F p q s (s ∈ ℝ, 0 < p < ∞, 0 < q ≤ ∞) on n . The aim of the paper is to clarify under what conditions f j | A p q s is equivalent to 2 j ( s - n / p ) ( k | a k | p ) 1 / p f | A p q s .

H p spaces associated with Schrödinger operators with potentials from reverse Hölder classes

Jacek Dziubański, Jacek Zienkiewicz (2003)

Colloquium Mathematicae

Similarity:

Let A = -Δ + V be a Schrödinger operator on d , d ≥ 3, where V is a nonnegative potential satisfying the reverse Hölder inequality with an exponent q > d/2. We say that f is an element of H A p if the maximal function s u p t > 0 | T t f ( x ) | belongs to L p ( d ) , where T t t > 0 is the semigroup generated by -A. It is proved that for d/(d+1) < p ≤ 1 the space H A p admits a special atomic decomposition.

A Diophantine inequality with four squares and one k th power of primes

Quanwu Mu, Minhui Zhu, Ping Li (2019)

Czechoslovak Mathematical Journal

Similarity:

Let k 5 be an odd integer and η be any given real number. We prove that if λ 1 , λ 2 , λ 3 , λ 4 , μ are nonzero real numbers, not all of the same sign, and λ 1 / λ 2 is irrational, then for any real number σ with 0 < σ < 1 / ( 8 ϑ ( k ) ) , the inequality | λ 1 p 1 2 + λ 2 p 2 2 + λ 3 p 3 2 + λ 4 p 4 2 + μ p 5 k + η | < max 1 j 5 p j - σ has infinitely many solutions in prime variables p 1 , p 2 , , p 5 , where ϑ ( k ) = 3 × 2 ( k - 5 ) / 2 for k = 5 , 7 , 9 and ϑ ( k ) = [ ( k 2 + 2 k + 5 ) / 8 ] for odd integer k with k 11 . This improves a recent result in W. Ge, T. Wang (2018).